# arXiv daily: Plasma Physics (physics.plasm-ph)

##### 1.Gamma-Flash Generation in Multi-Petawatt Laser-Matter Interactions

**Authors:**P. Hadjisolomou, T. M. Jeong, D. Kolenaty, A. J. Macleod, V. Olšovcová, R. Versaci, C. P. Ridgers, S. V. Bulanov

**Abstract:** The progressive development of high power lasers over the last several decades, enables the study of $\gamma$-photon generation when an intense laser beam interacts with matter, mainly via inverse Compton scattering at the high intensity limit. $\gamma$-ray flashes are a phenomenon of broad interest, drawing attention of researchers working in topics ranging from cosmological scales to elementary particle scales. Over the last few years, a plethora of studies predict extremely high laser energy to $\gamma$-photon energy conversion using various target and/or laser field configurations. The aim of the present manuscript is to discuss several recently proposed $\gamma$-ray flash generation schemes, as a guide for upcoming $\gamma$-photon related experiments and for further evolution of the presently available theoretical schemes.

##### 2.Phase space dynamics of unmagnetized plasmas: collisionless and collisional regimes

**Authors:**G. Celebre, S. Servidio, F. Valentini

**Abstract:** Eulerian electrostatic kinetic simulations of unmagnetized plasmas (kinetic electrons and motionless protons) with high-frequency equilibrium perturbations have been employed to investigate the phase space energy transfer across spatial and velocity scales, associated with the resonant interaction of electrons with the self-induced electric field. Numerical runs cover a wide range of collisionless and weakly collisional plasma regimes. An analysis technique based on the Fourier-Hermite transform of the particle distribution function allows to point out how kinetic processes trigger the phase space energy cascade, which is instead inhibited at finer scales when collisions are turned on. Numerical results are presented and discussed for the cases of linear wave Landau damping, nonlinear electron trapping, bump-on-tail and two-stream instabilities. A more realistic situation of turbulent Langmuir fluctuations is also discussed in detail. Fourier-Hermite transform shows an energy spread, highly conditioned by collisions, which involves velocity scales more quickly than the spatial scales, even when nonlinear effects are dominant. This results in anisotropic spectra whose slopes are compatible with theoretical expectations. Finally, an exact conservation law has been derived, which describes the time evolution of the free energy of the system, taking into account the collisional dissipation.

##### 3.Enhanced transport at high plasma $β$ and sub-threshold kinetic ballooning modes in Wendelstein 7-X

**Authors:**P. Mulholland
Eindhoven University of Technology, Eindhoven, The Netherlands, K. Aleynikova
Max-Planck-Institut für Plasmaphysik, Greifswald, Germany, B. J. Faber
University of Wisconsin-Madison, Madison, USA, M. J. Pueschel
Eindhoven University of Technology, Eindhoven, The Netherlands
Dutch Institute for Fundamental Energy Research, Eindhoven, The Netherlands, J. H. E. Proll
Eindhoven University of Technology, Eindhoven, The Netherlands, C. C. Hegna
University of Wisconsin-Madison, Madison, USA, P. W. Terry
University of Wisconsin-Madison, Madison, USA, C. Nührenberg
Max-Planck-Institut für Plasmaphysik, Greifswald, Germany

**Abstract:** The effect of plasma pressure $\beta$ on ion-temperature-gradient-driven (ITG) turbulence is studied in the Wendelstein 7-X (W7-X) stellarator, showing that subdominant kinetic ballooning modes (KBMs) are unstable well below the ideal MHD threshold and get strongly excited in the quasi-stationary state. By zonal-flow erosion, these highly non-ideal KBMs affect ITG saturation and thereby enable higher heat fluxes. Controlling these KBMs will be essential in order to allow W7-X and future stellarators to achieve maximum performance.

##### 4.Numerical validation of a volume heated mixed fuel reactor concept

**Authors:**Hartmut Ruhl, Georg Korn

**Abstract:** In earlier papers \cite{ruhlkornarXiv,ruhlkornarXiv1,ruhlkornarXiv2} the core elements of a novel direct drive $\text{pBDT}$ mixed fuel reactor without fuel pre-compression have been discussed. The predominant purpose of the mixed fuel is to chemically bind $\text{DT}$. It has been found that the proposed mixed fuel design can reach $Q_T > 1$ with $\text{MJ}$ level external isochoric heating and without fuel pre-compression due to a novel direct drive ultra-fast heating concept. In order to further validate the concept we make use of MULTI, an ICF community code, and show with the help of MULTI simulations that the semi-analytical scaling model presented in a previous paper is capable of making accurate predictions. The MULTI simulations yield $Q_T > 1$ for a $\text{pBDT}$ fuel mix at $\text{MJ}$ level isochoric preheating, which validates our theoretical model involving in-situ compression for $Q_T \gg 1$ at reduced overall heating requirements.

##### 5.Azimuthal ion movement in HiPIMS plasmas -- Part I: velocity distribution function

**Authors:**S. Thiemann-Monjé, J. Held, S. Schüttler, A. von Keudell, V. Schulz-von der Gathen

**Abstract:** Magnetron sputtering discharges feature complex magnetic field configurations to confine the electrons close to the cathode surface. This magnetic field configuration gives rise to a strong electron drift in azimuthal direction, with typical drift velocities on the order of \SI{100}{\kilo\meter\per\second}. In high power impulse magnetron sputtering (HiPIMS) plasmas, the ions have also been observed to follow the movement of electrons with velocities of a few \si{\kilo\meter\per\second}, despite being unmagnetized. In this work, we report on measurements of the azimuthal ion velocity using spatially resolved optical emission spectroscopy, allowing for a more direct measurement compared to experiments performed using mass spectrometry. The azimuthal ion velocities increase with target distance, peaking at about \SI{1.55}{\kilo\meter\per\second} for argon ions and \SI{1.25}{\kilo\meter\per\second} for titanium ions. Titanium neutrals are also found to follow the azimuthal ion movement which is explained with resonant charge exchange collisions. The experiments are then compared to a simple test-particle simulation of the titanium ion movement, yielding good agreement to the experiments when only considering the momentum transfer from electrons to ions via Coulomb collisions as the only source of acceleration in azimuthal direction. Based on these results, we propose this momentum transfer as the primary source for ion acceleration in azimuthal direction.

##### 6.Azimuthal ion movement in HiPIMS plasmas -- Part II: lateral growth fluxes

**Authors:**Steffen Schüttler, Sascha Thiemann-Monje, Julian Held, Achim von Keudell

**Abstract:** The transport of sputtered species from the target of a magnetron plasma to a collecting surface at the circumference of the plasma is analyzed using a particle tracer technique. A small chromium insert at the racetrack position inside a titanium target is used as the source of tracer particles, which are redeposited on the collecting surface. The azimuthal velocity of the ions along the racetrack above the target is determined from the Doppler shift of the optical emission lines of titanium and chromium. The trajectories are reconstructed from an analysis of the transport physics leading to the measured deposition profiles. It is shown that a simple direct-line-of sight re-deposition model can explain the data for low power plasmas (DCMS) and for pulsed high power impulse magnetron plasmas (HiPIMS) by using the Thompson velocity distribution from the sputter process as starting condition. In the case of a HiPIMS plasma, the drag force exerted on the ions and neutrals by the electron Hall current has to be included causing an azimuthal displacement in \ExB direction. Nevertheless, the Thompson sputter distribution remains preserved for 50\% of the re-deposited growth flux. The implications for the understanding of transport processes in magnetron plasmas are discussed.

##### 1.thermal and stress_strain analysis of the tested iter-like w langmuir probes in east

**Authors:**Chunyu He, Dahuan Zhu

**Abstract:** ITER-like tungsten Langmuir probes (W DLPs) have been installed and tested at the lower divertor horizontal target composed of flat-type components in EAST. Due to the non-active cooling, transient thermal and stress\strain analyses considering actual thermal loading and cooling conditions were thus conducted to evaluate the thermal performance and mechanical quality of W DLPs subjected to the long pulse & high plasma flux of EAST. The thermal analysis reveals that the inevitable leading edge induced thermal loading at surrounding area of W DLPs is not ignorable. The thermal performance of W DLPs are largely related to the plasma scenario (Qp: parallel heat flux along magnetic field line, {\alpha}: incline angle of magnetic field line). Under current plasma parameters, melting of W was not occurred in general, but recrystallization as well as the induced cracks may be still possible. And, the interval period (~1000 s) between neighboring shots is sufficient for nature cooling of W DLPs. The stress analysis also tells that the ceramic LLL may be general a crucial weak point of W DLPs, which is expected to not only limit the thermal affordability of long pulse but also cause possible crack problems. Such calculation results can provide important reference for current plasma operation and future improvement of the W DLPs.

##### 2.Reflectionless Plasma Ignition via High-Power Virtual Perfect Absorption

**Authors:**Théo Delage, Jérôme Sokoloff, Olivier Pascal, Valentin Mazières, Alex Krasnok, Thierry Callegari

**Abstract:** Plasma ignition is critical in various scientific and industrial applications, demanding an efficient and robust execution mechanism. In this work, we present an innovative approach to plasma ignition by incorporating the analysis of fundamental aspects of light scattering in the complex frequency plane. For the first time, we demonstrate the high-power virtual perfect absorption (VPA) regime, a groundbreaking method for perfectly capturing light within a resonator. By carefully designing the temporal profile of the incident wave, we effectively minimize reflections during the ignition stages, thereby significantly enhancing the efficiency and resilience of the process. Through comprehensive experimental investigations, we validate the viability of this approach, establishing VPA as a powerful tool for reflectionless excitation and optimal control of plasma discharge. By addressing the limitations of conventional plasma ignition methods, this research represents a pivotal step towards transformative advancements in plasma technology, with promising implications for improving the performance and sustainability of numerous applications.

##### 1.Direct Implicit and Explicit Energy-Conserving Particle-in-Cell Methods for Modeling of Capacitively-Coupled Plasma Devices

**Authors:**Haomin Sun, Soham Banerjee, Sarveshwar Sharma, Andrew Tasman Powis, Alexander V. Khrabrov, Dmytro Sydorenko, Jian Chen, Igor D. Kaganovich

**Abstract:** Achieving entire large scale kinetic modelling is a crucial task for the development and optimization of modern plasma devices. With the trend of decreasing pressure in applications such as plasma etching, kinetic simulations are necessary to self-consistently capture the particle dynamics. The standard, explicit, electrostatic, momentum-conserving Particle-In-Cell method suffers from tight stability constraints to resolve the electron plasma length (i.e. Debye length) and time scales (i.e. plasma period). This results in very high computational cost, making this technique generally prohibitive for the large volume entire device modeling (EDM). We explore the Direct Implicit algorithm and the explicit Energy Conserving algorithm as alternatives to the standard approach, which can reduce computational cost with minimal (or controllable) impact on results. These algorithms are implemented into the well-tested EDIPIC-2D and LTP-PIC codes, and their performance is evaluated by testing on a 2D capacitively coupled plasma discharge scenario. The investigation revels that both approaches enable the utilization of cell sizes larger than the Debye length, resulting in reduced runtime, while incurring only a minor compromise in accuracy. The methods also allow for time steps larger than the electron plasma period, however this can lead to numerical heating or cooling. The study further demonstrates that by appropriately adjusting the ratio of cell size to time step, it is possible to mitigate this effect to acceptable level.

##### 2.Combining stochastic density functional theory with deep potential molecular dynamics to study warm dense matter

**Authors:**Tao Chen, Qianrui Liu, Yu Liu, Liang Sun, Mohan Chen

**Abstract:** In traditional finite-temperature Kohn-Sham density functional theory (KSDFT), the well-known orbitals wall restricts the use of first-principles molecular dynamics methods at extremely high temperatures. However, stochastic density functional theory (SDFT) can overcome the limitation. Recently, SDFT and its related mixed stochastic-deterministic density functional theory, based on the plane-wave basis set, have been implemented in the first-principles electronic structure software ABACUS [Phys. Rev. B 106, 125132(2022)]. In this study, we combine SDFT with the Born-Oppenheimer molecular dynamics (BOMD) method to investigate systems with temperatures ranging from a few tens of eV to 1000 eV. Importantly, we train machine-learning-based interatomic models using the SDFT data and employ these deep potential models to simulate large-scale systems with long trajectories. Consequently, we compute and analyze the structural properties, dynamic properties, and transport coefficients of warm dense matter. The abovementioned methods offer a new approach with first-principles accuracy to tackle various properties of warm dense matter.

##### 1.Two-Dimensional Conformal Plasma Turbulence in the Hasegawa-Mima Equation

**Authors:**Shigeo Kawata

**Abstract:** The two-dimensional (2D) conformal field theory (CFT) suggests that the 2D plasma turbulence, governed by the Hasegawa-Mima (H-M) equation, may have multiple exponents of energy spectrum in momentum space. Electrostatic potential driven by drift waves in magnetized 2D plasmas would be described by the H-M equation. On the other hand, the 2D CFT has an infinite-dimensional symmetry. When we focus on minimal models established in 2D CFT, each minimal model provides a different 2D statistical model as presented in fluid turbulence, quantum field theory and string theory, and would provide a specific exponent of the energy spectrum. The CFT analytical results in this work suggests that the H-M plasma turbulence may have multiple exponents of the energy spectrum.

##### 2.Time-resolved optical shadowgraphy of solid hydrogen jets as a testbed to benchmark particle-in-cell simulations

**Authors:**Long Yang, Lingen Huang, Stefan Assenbaum, Thomas E Cowan, Ilja Goethel, Sebastian Göde, Thomas Kluge, Martin Rehwald, Xiayun Pan, Ulrich Schramm, Jan Vorberger, Karl Zeil, Tim Ziegler, Constantin Bernert

**Abstract:** Particle-in-cell (PIC) simulations are a superior tool to model kinetics-dominated plasmas in relativistic and ultrarelativistic laser-solid interactions (dimensionless vectorpotential $a_0 > 1$). The transition from relativistic to subrelativistic laser intensities ($a_0 \lesssim 1$), where correlated and collisional plasma physics become relevant, is reaching the limits of available modeling capabilities. This calls for theoretical and experimental benchmarks and the establishment of standardized testbeds. In this work, we develop such a suitable testbed to experimentally benchmark PIC simulations using a laser-irradiated micron-sized cryogenic hydrogen-jet target. Time-resolved optical shadowgraphy of the expanding plasma density, complemented by hydrodynamics and ray-tracing simulations, is used to determine the bulk-electron temperature evolution after laser irradiation. As a showcase, a study of isochoric heating of solid hydrogen induced by laser pulses with a dimensionless vectorpotential of $a_0 \approx 1$ is presented. The comparison of the bulk-electron temperature of the experiment with systematic scans of PIC simulations demostrates that, due to an interplay of vacuum heating and resonance heating of electrons, the initial surface-density gradient of the target is decisive to reach quantitative agreement at \SI{1}{\ps} after the interaction. The showcase demostrates the readiness of the testbed for controlled parameter scans at all laser intensities of $a_0 \lesssim 1$.

##### 3.Modulation of electromagnetic waves in a relativistic degenerate plasma at finite temperature

**Authors:**S. Roy, A. P. Misra, A. Abdikian

**Abstract:** We study the modulational instability (MI) of a linearly polarized electromagnetic (EM) wave envelope in an intermediate regime of relativistic degenerate plasmas at a finite temperature $(T\neq0)$ where the thermal energy $(K_BT)$ and the rest-mass energy $(m_ec^2)$ of electrons do not differ significantly, i.e., $\beta_e\equiv K_{B}T/m_{e}c^2\lesssim~(\rm{or}~\gtrsim) 1$, but, the Fermi energy $(K_BT_F)$ and the chemical potential energy $(\mu_e)$ of electrons are still a bit higher than the thermal energy, i.e., $T_F>T$ and $\xi_{e}=\mu_e/K_{B}T\gtrsim1$. Starting from a set of relativistic fluid equations for degenerate electrons at finite temperature, coupled to the EM wave equation and using the multiple scale perturbation expansion scheme, a one-dimensional nonlinear Sch{\"o}dinger (NLS) equation is derived, which describes the evolution of slowly varying amplitudes of EM wave envelopes. Then we study the MI of the latter in two different regimes, namely $\beta_e<1$ and $\beta_e>1$. Like unmagnetized classical cold plasmas, the modulated EM envelope is always unstable in the region $\beta_e>4$. However, for $\beta_e\lesssim1$ and $1<\beta_e<4$, the wave can be stable or unstable depending on the values of the EM wave frequency, $\omega$ and the parameter $\xi_e$. We also obtain the instability growth rate for the modulated wave and find a significant reduction by increasing the values of either $\beta_e$ or $\xi_e$. Finally, we present the profiles of the traveling EM waves in the form of bright (envelope pulses) and dark (voids) solitons, as well as the profiles (other than traveling waves) of the Kuznetsov-Ma breather, the Akhmediev breather, and the Peregrine solitons as EM rogue (freak) waves, and discuss their characteristics in the regimes of $\beta_e\lesssim1$ and $\beta_e>1$.

##### 4.Discharge characteristics of a low-pressure geometrically asymmetric cylindrical capacitively coupled plasma with an axisymmetric magnetic field

**Authors:**Swati Dahiya
Institute for Plasma Research, Bhat, Gujarat, India
Homi Bhabha National Institute, Training School Complex, Mumbai, India and, Pawandeep Singh
Institute for Plasma Research, Bhat, Gujarat, India
Homi Bhabha National Institute, Training School Complex, Mumbai, India and, Yashashri Patil
Institute for Plasma Research, Bhat, Gujarat, India, Sarveshwar Sharma
Institute for Plasma Research, Bhat, Gujarat, India
Homi Bhabha National Institute, Training School Complex, Mumbai, India and, Nishant Sirse
Institute of Science and Research and Centre for Scientific and Applied Research, IPS Academy, Indore, India, Shantanu Kumar Karkari
Institute for Plasma Research, Bhat, Gujarat, India
Homi Bhabha National Institute, Training School Complex, Mumbai, India and

**Abstract:** We investigate the discharge characteristics of a low-pressure geometrically asymmetric cylindrical capacitively coupled plasma discharge with an axisymmetric magnetic field generating an EXB drift in the azimuthal direction. Vital discharge parameters, including electron density, electron temperature, DC self-bias, and Electron Energy distribution function (EEDF), are studied experimentally for varying magnetic field strength (B). A transition in the discharge asymmetry is observed along with a range of magnetic fields where the discharge is highly efficient with lower electron temperature. Outside this range of magnetic field, the plasma density drops, followed by an increase in the electron temperature. The observed behavior is attributed to the transition from geometrical asymmetry to magnetic field-associated symmetry due to reduced radial losses and plasma confinement in the peripheral region. In this region, the DC self-bias increases almost linearly from a large negative value to nearly zero, i.e., the discharge becomes symmetric. The EEDF undergoes a transition from bi-Maxwellian for unmagnetized to Maxwellian at intermediate B and finally becomes a weakly bi-Maxwellian at higher values of B. The above transitions present a novel way to independently control the ion energy and ion flux in a cylindrical CCP system using an axisymmetric magnetic field with an enhanced plasma density and lower electron temperature operation that is beneficial for plasma processing applications.

##### 5.Fast transport simulations with higher-fidelity surrogate models for ITER

**Authors:**J. Citrin, P. Trochim, T. Goerler, D. Pfau, K. L. van de Plassche, F. Jenko

**Abstract:** A fast and accurate turbulence transport model based on quasilinear gyrokinetics is developed. The model consists of a set of neural networks trained on a bespoke quasilinear GENE dataset, with a saturation rule calibrated to dedicated nonlinear simulations. The resultant neural network is approximately eight orders of magnitude faster than the original GENE quasilinear calculations. ITER predictions with the new model project a fusion gain in line with ITER targets. While the dataset is currently limited to the ITER baseline regime, this approach illustrates a pathway to develop reduced-order turbulence models both faster and more accurate than the current state-of-the-art.

##### 6.SDR, EVC, and SDREVC: Limitations and Extensions

**Authors:**E. D. Hunter, C. Amsler, H. Breuker, M. Bumbar, S. Chesnevskaya, G. Costantini, R. Ferragut, M. Giammarchi, A. Gligorova, G. Gosta, H. Higaki, C. Killian, V. Kraxberger, N. Kuroda, A. Lanz, M. Leali, G. Maero, C. Malbrunot, V. Mascagna, Y. Matsuda, V. Mäckel, S. Migliorati, D. J. Murtagh, A. Nanda, L. Nowak, F. Parnefjord Gustafsson, S. Rheinfrank, M. Romé, M. C. Simon, M. Tajima, V. Toso, S. Ulmer, L. Venturelli, A. Weiser, E. Widmann, Y. Yamazaki, J. Zmeskal

**Abstract:** Methods for reducing the radius, temperature, and space charge of nonneutral plasma are usually reported for conditions which approximate an ideal Penning Malmberg trap. Here we show that (1) similar methods are still effective under surprisingly adverse circumstances: we perform SDR and SDREVC in a strong magnetic mirror field using only 3 out of 4 rotating wall petals. In addition, we demonstrate (2) an alternative to SDREVC, using e-kick instead of EVC and (3) an upper limit for how much plasma can be cooled to T < 20 K using EVC. This limit depends on the space charge, not on the number of particles or the plasma density.

##### 1.On the capillary discharge in the high repetition rate regime

**Authors:**P. Sasorov, G. Bagdasarov, N. Bobrova, G. Grittani, A. Molodozhentsev, S. V. Bulanov

**Abstract:** We investigate the main physical processes that limit the repetition rate of capillary discharges used in laser accelerators of electrons theoretically and with computer simulations. We consider processes in the capillary. We assume that a cooling system independently maintains temperature balance of the capillary, as well as a gas supply system and a vacuum system maintain conditions outside the capillary. The most important factor, determining the highest repetition rates in this case, is the capillary length, which governs a refilling time of the capillary by the gas. For a short capillary, used for acceleration of sub-GeV electron beams, the repetition rate approximately equal to 10 kHz, which is inversely proportional to the square of the capillary length. The effects of the capillary diameter, gas type and the gas density are weaker.

##### 2.Effect of flow shear on the onset of dynamos

**Authors:**Shishir Biswas, Rajaraman Ganesh

**Abstract:** Understanding the origin and structure of mean magnetic fields in astrophysical conditions is a major challenge. Shear flows often coexist in such astrophysical conditions and the role of flow shear on dynamo mechanism is only beginning to be investigated. Here, we present a direct numerical simulation (DNS) study of the effect of flow shear on dynamo instability for a variety of base flows with controllable mirror symmetry (i.e, fluid helicity). Our observations suggest that for helical base flow, the effect of shear is to suppress the small scale dynamo (SSD) action, i.e, shear helps the large scale magnetic field to manifest itself by suppressing SSD action. For non-helical base flows, flow shear has the opposite effect of amplifying the small-scale dynamo action. The magnetic energy growth rate ($\gamma$) for non-helical base flows are found to follow an algebraic nature of the form, $\gamma = - aS + bS^\frac{2}{3}$ , where a, b > 0 are real constants and S is the shear flow strength and $\gamma$ is found to be independent of scale of flow shear. Studies with different shear profiles and shear scale lengths for non-helical base flows have been performed to test the universality of our finding.

##### 1.Fast Dynamic 1D Simulation of Divertor Plasmas with Neural PDE Surrogates

**Authors:**Yoeri Poels, Gijs Derks, Egbert Westerhof, Koen Minartz, Sven Wiesen, Vlado Menkovski

**Abstract:** Managing divertor plasmas is crucial for operating reactor scale tokamak devices due to heat and particle flux constraints on the divertor target. Simulation is an important tool to understand and control these plasmas, however, for real-time applications or exhaustive parameter scans only simple approximations are currently fast enough. We address this lack of fast simulators using neural PDE surrogates, data-driven neural network-based surrogate models trained using solutions generated with a classical numerical method. The surrogate approximates a time-stepping operator that evolves the full spatial solution of a reference physics-based model over time. We use DIV1D, a 1D dynamic model of the divertor plasma, as reference model to generate data. DIV1D's domain covers a 1D heat flux tube from the X-point (upstream) to the target. We simulate a realistic TCV divertor plasma with dynamics induced by upstream density ramps and provide an exploratory outlook towards fast transients. State-of-the-art neural PDE surrogates are evaluated in a common framework and extended for properties of the DIV1D data. We evaluate (1) the speed-accuracy trade-off; (2) recreating non-linear behavior; (3) data efficiency; and (4) parameter inter- and extrapolation. Once trained, neural PDE surrogates can faithfully approximate DIV1D's divertor plasma dynamics at sub real-time computation speeds: In the proposed configuration, 2ms of plasma dynamics can be computed in $\approx$0.63ms of wall-clock time, several orders of magnitude faster than DIV1D.

##### 1.Phase transition of three-dimensional finite-sized charged dust clusters in a plasma environment

**Authors:**Hirakjyoti Sarma, Ritupan Sarmah, Nilakshi Das

**Abstract:** The dynamics of a harmonically trapped three-dimensional Yukawa ball of charged dust particles immersed in plasma is investigated as function of external magnetic field and Coulomb coupling parameter using molecular dynamics simulation. It is shown that the harmonically trapped dust particles organize themselves into nested spherical shells. The particles start rotating in a coherent order as the magnetic field reaches a critical value corresponding to the coupling parameter of the system of dust particles. The magnetically controlled charged dust cluster of finite size undergoes a first-order phase transition from disordered to ordered phase. At sufficiently high coupling and strong magnetic field, the vibrational mode of this finite-sized charged dust cluster freezes, and the system retains only rotational motion.

##### 2.Energy loss enhancement of very intense proton beams in dense matter due to the beam-density effect

**Authors:**Benzheng Chen, Jieru Ren, Zhigang Deng, Wei Qi, Zhongmin Hu, Bubo Ma, Xing Wang, Shuai Yin, Jianhua Feng, Wei Liu, Zhongfeng Xu, Dieter H. H. Hoffmann, Shaoyi Wang, Quanping Fan, Bo Cui, Shukai He, Zhurong Cao, Zongqing Zhao, Leifeng Cao, Yuqiu Gu, Shaoping Zhu, Rui Cheng, Xianming Zhou, Guoqing Xiao, Hongwei Zhao, Yihang Zhang, Zhe Zhang, Yutong Li, Weimin Zhou, Yongtao Zhao

**Abstract:** Thoroughly understanding the transport and energy loss of intense ion beams in dense matter is essential for high-energy-density physics and inertial confinement fusion. Here, we report a stopping power experiment with a high-intensity laser-driven proton beam in cold, dense matter. The measured energy loss is one order of magnitude higher than the expectation of individual particle stopping models. We attribute this finding to the proximity of beam ions to each other, which is usually insignificant for relatively-low-current beams from classical accelerators. The ionization of the cold target by the intense ion beam is important for the stopping power calculation and has been considered using proper ionization cross section data. Final theoretical values agree well with the experimental results. Additionally, we extend the stopping power calculation for intense ion beams to plasma scenario based on Ohm's law. Both the proximity- and the Ohmic effect can enhance the energy loss of intense beams in dense matter, which are also summarized as the beam-density effect. This finding is useful for the stopping power estimation of intense beams and significant to fast ignition fusion driven by intense ion beams.

##### 1.A relativistic two-stream instability in an extremely low-density plasma

**Authors:**Shinji Koide, Masaaki Takahashi, Rohta Takahashi

**Abstract:** A linear analysis based on two-fluid equations in the approximation of a cold plasma, wherein the plasma temperature is assumed to be zero, demonstrates that a two-stream instability occurs in all cases. However, if this were true, the drift motion of electrons in an electric current over a wire would become unstable, inducing an oscillation in an electric circuit with ions bounded around specific positions. To avoid this peculiar outcome, we must assume a warm plasma with a finite temperature when discussing the criterion of instability. The two-stream instability in warm plasmas has typically been analyzed using kinetic theory to provide a general formula for the instability criterion from the distribution function of the plasma. However, the criteria based on kinetic theory do not have an easily applicable form. Here, we provide an easily applicable criterion for the instability based on the two-fluid model at finite temperatures, extensionally in the framework of special relativity. This criterion is relevant for analyzing two-stream instabilities in low-density plasmas in the universe and in Earth-based experimental devices.

##### 2.Guiding Center Derivation of the Generalized Hasegawa-Mima Equation for Drift Wave Turbulence in Curved Magnetic Fields

**Authors:**Naoki Sato, Michio Yamada

**Abstract:** Recently, a generalized Hasegawa-Mima (gHM) equation describing drift wave turbulence in curved magnetic fields has been derived in [N. Sato and M. Yamada, J. Plasma Phys. (2022), vol. 88, 905880319] for an ion-electron plasma modeled as a two-fluid system. In this work, we show that a mathematically equivalent GHM equation can be obtained within the kinetic framework of guiding center motion, and that the relevant drift wave turbulence ordering can be further relaxed, effectively generalizing the applicability of the equation to any magnetic field geometry and electron spatial density, in the sense that no ordering requirements involve spatial derivatives of the magnetic field or the electron spatial density.

##### 3.Hamiltonian Structure and Nonlinear Stability of Steady Solutions of the Generalized Hasegawa-Mima Equation for Drift Wave Turbulence in Curved Magnetic Fields

**Authors:**Naoki Sato, Michio Yamada

**Abstract:** The Generalized Hasegawa-Mima (GHM) equation, which generalizes the standard Hasegawa-Mima (HM) equation, is a nonlinear equation describing the evolution of drift wave turbulence in curved magnetic fields. The GHM equation can be obtained from a drift wave turbulence ordering that does not involve ordering conditions on spatial derivatives of the magnetic field or the plasma density, and it is therefore appropriate to describe the evolution of electrostatic turbulence in strongly inhomogeneous magnetized plasmas. In this work, we discuss the noncanonical Hamiltonian structure of the GHM equation, and obtain conditions for the nonlinear stability of steady solutions through the energy-Casimir stability criterion. These results are then applied to describe drift waves and infer the existence of stable toroidal zonal flows with radial shear in dipole magnetic fields.

##### 4.Quantum Description of Free Electron Laser Radiation and Nonlinear Amplitude Equations

**Authors:**Stephan I. Tzenov, Zhichu Chen

**Abstract:** A relativistic quantum mechanical model to describe the quantum FEL dynamics has been developed. Neglecting the spin of electrons in the impacting beam, this model is based on the Klein-Gordon equation coupled to the Poisson equation for the space-charge potential and the wave equation for the transverse components of the radiation field. Furthermore, a system of coupled nonlinear envelope equations for the slowly varying amplitudes of the electron beam distribution and the radiation field has been derived. The fundamental system of basic equations have been cast into a suitable hydrodynamic formulation. In the framework of the hydrodynamic representation, a new dispersion relation has been derived and analyzed in both the quantum and the quasi-classical regimes, where the space-charge oscillations of the electron beam are taken into account.

##### 5.Demonstration of tunability of HOFI waveguides via start-to-end simulations

**Authors:**S. M. Mewes, G. J. Boyle, A. Ferran Pousa, R. J. Shalloo, J. Osterhoff, C. Arran, L. Corner, R. Walczak, S. M. Hooker, M. Thévenet

**Abstract:** In recent years, hydrodynamic optical-field-ionized (HOFI) channels have emerged as a promising technique to create laser waveguides suitable for guiding tightly-focused laser pulses in a plasma, as needed for laser-plasma accelerators. While experimental advances in HOFI channels continue to be made, the underlying mechanisms and the roles of the main parameters remain largely unexplored. In this work, we propose a start-to-end simulation pipeline of the HOFI channel formation and the resulting guiding properties, and use it to explore the underlying physics and the tunability of HOFI channels. This approach is benchmarked against experimental measurements. HOFI channels are shown to feature excellent guiding properties over a wide range of parameters, making them a promising and tunable waveguide option for laser-plasma accelerators.

##### 6.Nonlinear saturation of resistive tearing modes in a cylindrical tokamak with and without solving the dynamics

**Authors:**J. Loizu, D. Bonfiglio

**Abstract:** We show that the saturation of resistive tearing modes in a cylindrical tokamak, as well as the corresponding island width, can be directly calculated with an MHD equilibrium code without solving the dynamics and without considering resistivity. The results are compared to initial value resistive MHD simulations and to an analytical nonlinear theory. For small enough islands, the agreement is remarkable. For sufficiently large islands, the equilibrium calculations, which assume a flat current profile inside the island, overestimate the saturation amplitude. On the other hand, excellent agreement between nonlinear resistive MHD simulations and nonlinear theory is observed for all the considered tearing unstable equilibria.

##### 7.Reduction (or enhancement) of stellarator turbulence by impurities

**Authors:**J. M. García-Regaña, I. Calvo, F. I. Parra, H. Thienpondt

**Abstract:** A systematic study of the impact of impurities on the turbulent heat fluxes is presented for Wendelstein 7-X. By means of nonlinear multispecies gyrokinetic simulations, it is shown that impurities, depending on the sign of their density gradient, can significantly enhance or reduce turbulent heat losses. For the relevant scenario of turbulence reduction, heat fluxes have a local minimum at a certain impurity concentration. This result demonstrates the potential of impurities for controlling turbulence and accessing enhanced confinement regimes in stellarators.

##### 8.Magnetized dusty plasma: On issues of its complexity and magnetization of charged dust particles

**Authors:**Mangilal Choudhary

**Abstract:** It is possible to excite various linear and non-linear low-frequency modes in dusty plasma which is an admixture of electrons, ions, gas atoms, and negatively charged solid particles. The experimental as well as theoretical study of these low-frequency dynamical modes in dusty plasma is very complex because of the involvement of dynamics of electrons, ions, and neutrals. If the external magnetic field is introduced to dusty plasma then the dynamics of it will be more complex. The complexity of magnetized dusty plasma where plasma species are magnetized is discussed by keeping the experimental observations in magnetized dusty plasma devices in mind. The requirement of theoretical modeling, as well as computation experiments in understanding the dynamics of dusty plasma in the presence of a strong magnetic field, is highlighted in the context of experimental findings. The major challenges to magnetizing charged massive particles in experiments and some expected solutions are discussed in this report.

##### 1.Rotating spokes, potential hump and modulated ionization in radio frequency magnetron discharges

**Authors:**Liang Xu, Haoming Sun, Denis Eremin, Sathya Ganta, Igor Kaganovich, Kallol Bera, Shahid Rauf

**Abstract:** In this work, the rotating spoke mode in the radio frequency (RF) magnetron discharge, which features the potential hump and the RF-modulated ionization, is observed and analyzed by means of the two dimensional axial-azimuthal (z-y) particle-in-cell/Monte Carlo collision method. The kinetic model combined with the linear analysis of the perturbation reveals that the cathode sheath (axial) electric field $E_z$ triggers the gradient drift instability (GDI), deforming the local potential until the instability condition is not fulfilled and the fluctuation growth stops in which moment the instability becomes saturated. The potential deformation consequently leads to the formation of the potential hump, surrounding which the azimuthal electric field $E_y$ is present. The saturation level of $E_y$ is found to be synchronized with and proportional to the time-changing voltage applied at the cathode, resulting in the RF-modulation of the electron heating in the $E_y$ due to $\nabla B$ drift. In the instability saturated stage, it is shown that the rotation velocity and direction of the spoke present in the simulations agree well with the experimental observation. In the instability linear stage, the instability mode wavelength and the growth rate are also found to be in good agreement with the prediction of the GDI linear fluid theory.

##### 2.The Nonlinear Evolution of Whistler-Mode Chorus Revisited: Modulation Instability as the Source of Tones

**Authors:**Daniel Ratliff, Oliver Allanson

**Abstract:** We review the modulation stability of parallel propagating/field aligned Whistler Mode Chorus waves propagating in a warm plasma from a formal perspective with a focus on wave-particle interactions. The modulation instability criteria is characterised by a curvature of the dispersion relation for Whistler mode waves and a condition on the ratio between the group velocity $c_g$ and the electron sound speed $c_{s,e}$. We also demonstrate the in order to investigate the spatiotemporal evolution of the envelope and the formation of packets, one necessarily needs to account for the motion of ions within the system, leading to an ionic influence on the modulation instability threshold determined by the ion fraction of the plasma. Finally, we demonstrate that chirping may be captured when higher order effects are included within the spatiotemporal evolution of the amplitude. This yields not only an explicit expression for the sweep rate but identifies a possible origin for the power band gap that occurs at half the electron gyrofrequency. Numerical validation demonstrates that the interaction between wave packets is a source for the emergence of tones observed within mission data, and such interactions may be a major source of the electron energisation which Whistler-Mode chorus are responsible for.

##### 1.X-ray Thomson scattering absolute intensity from the f-sum rule in the imaginary-time domain

**Authors:**Tobias Dornheim, Tilo Döppner, Andrew D. Baczewski, Panagiotis Tolias, Maximilian P. Böhme, Zhandos A. Moldabekov, Divyanshu Ranjan, David A. Chapman, Michael J. MacDonald, Thomas R. Preston, Dominik Kraus, Jan Vorberger

**Abstract:** We evaluate the f-sum rule on the dynamic structure factor in the imaginary-time domain as a formally exact and simulation-free means of normalizing X-Ray Thomson Scattering (XRTS) spectra. This circumvents error-prone real-time deconvolution of the source function and facilitates calculating the static structure factor from the properly normalized imaginary-time correlation function. We apply our technique to two distinct sets of experimental data, finding that it is effective for both narrow and broad x-ray sources. This approach could be readily adapted to other scattering spectroscopies.

##### 1.Effect of electron-beam energy chirp on signatures of radiation reaction in laser-based experiments

**Authors:**J. Magnusson, T. G. Blackburn, E. Gerstmayr, E. E. Los, M. Marklund, C. P. Ridgers, S. P. D. Mangles

**Abstract:** Current experiments investigating radiation reaction employ high energy electron beams together with tightly focused laser pulses in order to reach the quantum regime, as expressed through the quantum nonlinearity parameter $\chi$. Such experiments are often complicated by the large number of latent variables, including the precise structure of the electron bunch. Here we examine a correlation between the electron spatial and energy distributions, called an energy chirp, investigate its significance to the laser-electron beam interaction and show that the resulting effect cannot be trivially ignored when analysing current experiments. In particular, we show that the energy chirp has a large effect on the second moment of the electron energy, but a lesser impact on the first electron energy moment or the photon critical energy. These results show the importance of improved characterisation and control over electron bunch parameters on a shot-to-shot basis in such experiments.

##### 1.Accelerated Bayesian inference of plasma profiles with self-consistent MHD equilibria at W7-X via neural networks

**Authors:**Andrea Merlo, Andrea Pavone, Daniel Böckenhoff, Ekkehard Pasch, Golo Fuchert, Kai Jakob Brunner, Kian Rahbarnia, Jonathan Schilling, Udo Höfel, Sehyun Kwak, Jakob Svensson, Thomas Sunn Pedersen, the W7-X team

**Abstract:** High-$\langle \beta \rangle$ operations require a fast and robust inference of plasma parameters with a self-consistent MHD equilibrium. Precalculated MHD equilibria are usually employed at W7-X due to the high computational cost. To address this, we couple a physics-regularized NN model that approximates the ideal-MHD equilibrium with the Bayesian modeling framework Minerva. We show the fast and robust inference of plasma profiles (electron temperature and density) with a self-consistent MHD equilibrium approximated by the NN model. We investigate the robustness of the inference across diverse synthetic W7-X plasma scenarios. The inferred plasma parameters and their uncertainties are compatible with the parameters inferred using the VMEC, and the inference time is reduced by more than two orders of magnitude. This work suggests that MHD self-consistent inferences of plasma parameters can be performed between shots.

##### 1.Laser harmonic generation with tuneable orbital angular momentum using a structured plasma target

**Authors:**R. M. G. M. Trines, H. Schmitz, M. King, P. McKenna, R. Bingham

**Abstract:** In previous studies of spin-to-orbital angular momentum (AM) conversion in laser high harmonic generation (HHG) using a plasma target, one unit of spin AM is always converted into precisely one unit of OAM [1, 2]. Here we show, through analytic theory and numerical simulations, that we can exchange one unit of SAM for a tuneable amount of OAM per harmonic step, via the use of a structured plasma target. In the process, we introduce a novel framework to study laser harmonic generation via recasting it as a beat wave process. This framework enables us to easily calculate and visualise harmonic progressions, unify the "photon counting" and "symmetry-based" approaches to HHG and provide new explanations for existing HHG results. Our framework also includes a specific way to analyse simultaneously the frequency, spin and OAM content of the harmonic radiation which provides enhanced insight into this process. The prospects of using our new framework to design HHG configurations with tuneable high-order transverse modes, also covering the design of structured plasma targets, will be discussed.

##### 1.Analysis of ion-acoustic rogue wave in complex magneto-plasmas

**Authors:**A. Parvez

**Abstract:** I considered a four-component magnetized plasma medium consisting of opposite polarity ions and super-thermal distributed positrons and electrons to investigate the stable/unstable frequency regimes of modulated ion-acoustic waves (IAWs) in the D-F regions of Earth's ionosphere and laboratory plasmas. A $(3+1)$-dimensional nonlinear Schr\"{o}dinger equation is derived. The parametric regimes for the existence of the MI, first- and second-order rogue waves, and also their basic features (viz., amplitude, width, and speed) are found to be significantly modified by the effect of physical plasma parameters (such as superthermal index and positron to electron temperature ratio) and external magnetic field. It is found that the nonlinearity of the different types of electronegative plasma system depends on the positive to negative ion mass ratio. It is also shown that the presence of super-thermal distributed electrons and positrons modifies the nature of the MI of the modulated IAWs. The implication of our results for the laboratory plasma [e.g., ($Ar^+,~F^-$) electronegative plasma] and space plasma [e.g., ($H^+,~H^-$), ($H^+,~O_2^-$) electronegative plasma in D-F regions of Earth's ionosphere] are briefly discussed.

##### 1.Applicability of the Klein-Gordon equation for pair production in vacuum and plasma

**Authors:**Haidar Al-Naseri, Gert Brodin

**Abstract:** In this paper, a phase-space description of electron-positron pair-creation will be applied, based on a Wigner transformation of the Klein-Gordon equation. The resulting theory is similar in many respects to the equations from the Dirac-Heisenberg-Wigner formalism. However, in the former case, all physics related to particle spin is neglected. In the present paper we compare the pair-production rate in vacuum and plasmas, with and without spin effects, in order to evaluate the accuracy and applicability of the spinless approximation. It is found that for modest frequencies of the electromagnetic field, the pair production rate of the Klein-Gordon theory is a good approximation to the Dirac theory, provided the matter density is small enough for Pauli blocking to be neglected, and a factor of two related to the difference in the vacuum energy density is compensated for.

##### 2.X-ray absorption spectroscopy using an ultrafast laboratory-scale laser-plasma accelerator source

**Authors:**B. Kettle, C. Colgan, E. Los, E. Gerstmayr, M. J. V. Streeter, F. Albert, S. Astbury, R. A. Baggott, N. Cavanagh, K. Falk, T. I. Hyde, O. Lundh, P. P. Rajeev, D. Riley, S. J. Rose, G. Sarri, C. Spindloe, K. Svendsen, D. R. Symes, M. Smid, A. G. R. Thomas, C. Thornton, R. Watt, S. P. D. Mangles

**Abstract:** The absorption profile of the copper K-edge was measured over a 250 eV window using ultrashort X-rays from a laser-plasma wakefield accelerator. For the first time with a femtosecond probe, Extended X-ray Absorption Fine Structure (EXAFS) features were observed in a single shot, detailing the local atomic structure. This unique capability will allow the investigation of novel ultrafast processes, and in particular probing high energy density matter and physics far-from-equilibrium. A perspective on the additional strengths of a laboratory-based ultrafast X-ray absorption source is presented.

##### 3.Evolution of Coupled Weakly-Driven Waves in a Dissipative Plasma

**Authors:**N. M. Pham, V. N. Duarte

**Abstract:** The nonlinear collisional dynamics of coupled driven plasma waves in the presence of background dissipation is studied analytically within kinetic theory. Sufficiently near marginal stability, phase space correlations are poorly preserved and time delays become unimportant. The system is then shown to be governed by two first-order coupled autonomous differential equations of cubic order for the wave amplitudes and two complementary first-order equations for the evolution of their phases. That system of equations can be decoupled and further simplified to a single second-order differential equation of Li\'enard's type for each amplitude. Numerical solutions for this equation are obtained in the general case while analytic solutions are obtained for special cases in terms of parameters related to the spacing of the resonances of the two waves in frequency space, e.g., wave lengths and oscillation frequencies. These parameters are further analyzed to find classes of quasi-steady saturation and pulsating scenarios. To classify equilibrium points, local stability analysis is applied, and bifurcation conditions are determined. When the two waves saturate at similar amplitude levels, their combined signal is shown to invariably exhibit amplitude beating and phase jumps of nearly $\pi$. The obtained analytical results can be used to benchmark simulations and to interpret eigenmode amplitude measurements in fusion experiments.

##### 1.Non-LTE ionization potential depression model for warm and hot dense plasma

**Authors:**Chensheng Wu, Fuyang Zhou, Yong Wu, Jun Yan, Xiang Gao, Jianguo Wang

**Abstract:** For warm and hot dense plasma (WHDP), the ionization potential depression (IPD) is a key physical parameter in determining its ionization balance, therefore a reliable and universal IPD model is highly required to understand its microscopic material properties and resolve those existing discrepancies between the theoretical and experimental results. However, the weak temperature dependence of the nowadays IPD models prohibits their application through much of the WHDP regime, especially for the non-LTE dense plasma produced by short-pulse laser. In this work, we propose a universal non-LTE IPD model with the contribution of the inelastic atomic processes, and found that three-body recombination and collision ionization processes become important in determining the electron distribution and further affect the IPD in warm and dense plasma. The proposed IPD model is applied to treat the IPD experiments available in warm and hot dense plasmas and excellent agreements are obtained in comparison with those latest experiments of the IPD for Al plasmas with wide-range conditions of 70-700 eV temperature and 0.2-3 times of solid density, as well as a typical non-LTE system of hollow Al ions. We demonstrate that the present IPD model has a significant temperature dependence due to the consideration of the inelastic atomic processes. With the low computational cost and wide range applicability of WHDP, the proposed model is expected to provide a promising tool to study the ionization balance and the atomic processes as well as the related radiation and particle transports properties of a wide range of WHDP.

##### 2.2D electromagnetic simulations of RF heating via inductive coupling in the SPIDER device

**Authors:**D. López-Bruna, P. Jain, M. Recchia, B. Zaniol, E. Sartori, C. Poggi, V. Candeloro, G. Serianni, P. Veltri

**Abstract:** SPIDER is the prototype ion source of MITICA, the full-size neutral beam heating system conceived for the ITER tokamak. It includes eight drivers to heat and sustain the inductively coupled plasma (ICP). Owing to their near cylindrical symmetry, the coupling between the radio-frequency (RF) active currents and the source plasma is studied using a 2D electromagnetic approach with simplified expressions for the plasma electrical conductivity taken from the literature. The power absorbed by the plasma and the effect of the induced plasma currents in lowering the inductance of the driver are based on data from the dedicated S16 experimental campaign (y.~2020) of SPIDER: plasma electron densities on the order of $10^{18}$ m$^{-3}$, electron temperatures $\sim 10$ eV; neutral gas pressure $\sim 0.3$ Pa and up to $50$ kW of net power per driver. It is found that the plasma conductivity cannot be explained by the friction forces associated to local collisional processes alone. The inclusion of an effective collisionality associated to non-local processes seems also insufficient to explain the experimental information. Only when the electrical conductivity is reduced where the RF magnetic field is more intense, can the heating power and driver inductance be acceptably reproduced. We present the first 2D electromagnetic ICP calculations in SPIDER for two types of plasma, without and with the addition of a static magnetic field. The power transfer efficiency to the plasma of the first drivers of SPIDER, in view of these models, is around 50%

##### 3.On propagation of positive and negative streamers in air in uniform electric fields

**Authors:**G V Naidis, N Yu Babaeva

**Abstract:** Recently published results of numerical simulations of positive and negative streamers propagating in uniform electric fields in air are analyzed here in the framework of an analytical approach. Obtained approximate relations between the streamer radius, velocity and length, depending on the value of applied electric field, are in reasonable agreement with the results of numerical simulations.

##### 1.Spectral-partitioned Kohn-Sham density functional theory

**Authors:**Babak Sadigh, Daniel Aberg, John Pask

**Abstract:** We introduce a general, variational scheme applied to Kohn-Sham density functional theory that allows for partitioning of the ground-state density matrix into distinct spectral domains, each of which spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact one, attaining this limit as representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for effective calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multi-projector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

##### 2.The role of magnetic helicity when it is absent on average

**Authors:**Axel Brandenburg, Gustav Larsson

**Abstract:** Magnetic helicity plays a tremendously important role when it is different from zero on average. Most notably, it leads to the phenomenon of an inverse cascade. Here, we consider decaying magnetohydrodynamic turbulence as well as some less common examples of magnetic evolution under the Hall effect and ambipolar diffusion, as well as cases in which the magnetic field evolution is constrained by the presence of an asymmetry in the number density of chiral fermions, whose spin is systematically either aligned or anti-aligned with its momentum. In all those cases, there is a new conserved quantity: the Hosking integral. We present quantitative scaling results for the magnetic integral scale as well as the magnetic energy density and its spectrum. We also compare with cases were also a magnetic version of the Saffman integral is initially finite.

##### 1.Elevating 0-D global scaling predictions to self-consistent theory-based simulations

**Authors:**Tim Slendebroek, Joseph McClenaghan, Orso Meneghini, Brendan C. Lyons, Sterling P. Smith, Tom F. Neiser, Nan Shi, Jeff Candy

**Abstract:** A new workflow in the OMFIT integrated modelling framework (STEP-0D) has been developed to make theory-based prediction of tokamak scenarios starting from zero-dimensional (0D) quantities. The workflow starts with the PRO-create (profiles creator) module, which generates physically plausible plasma profiles and a consistent equilibrium from the same 0D quantities as the IPB98(y,2) confinement scaling. These results form the starting point for the STEP (Stability, Transport, Equilibrium, and Pedestal) module, which then iterates between state-of-the-art theory-based physics models for the equilibrium, core transport, and pedestal to obtain a self-consistent solution. A systematic validation against the International Tokamak Physics Activity (ITPA) global H-mode confinement database demonstrated that on average STEP-0D is capable of predicting the energy confinement time with a mean relative error (MRE) <19%. The validated workflow was used to predict proposed fusion reactor plasmas finding moderate H-factors between 0.9 and 1.2 its further use will be instrumental for the prediction of the plasma performance of a viable fusion power plant and is being utilized in design studies.

##### 2.3D modeling of positive streamers in air with inhomogeneous density

**Authors:**Baohong Guo, Ute Ebert, Jannis Teunissen

**Abstract:** We study the effect of an inhomogeneous gas density on positive streamer discharges in air using a 3D fluid model with stochastic photoionization, generalizing earlier work with a 2D axisymmetric model by Starikovskiy and Aleksandrov (2019 Plasma Sources Sci. Technol. 28 095022). We consider various types of planar and (hemi)spherical gas density gradients, focusing on the case in which streamers propagate from a region of density n0 towards a region of higher gas density, where n0 corresponds to 300 K and 1 bar. We observe streamer branching at the density gradient, with branches growing in a flower-like pattern over the gradient surface. Depending on the gas density ratio, the gradient width and other factors, narrow branches are able to propagate into the higher-density gas. In a planar geometry, we find that such propagation is possible up to a gas density slope of 3.5n0/mm, although this value depends on a number of conditions, such as the gradient angle. Surprisingly, a higher applied voltage makes it more difficult for streamers to penetrate into the high-density region, due to an increase of the primary streamer's radius.

##### 1.Diagnosis of Fast Electron Transport by Coherent Transition Radiation

**Authors:**Yangchun Liu, Xiaochuan Ning, Dong Wu, Tianyi Liang, Peng Liu, Shujun Liu, Xu Liu, Zhengmao Sheng, Wei Hong, Yuqiu Gu, Xiantu He

**Abstract:** Transport of fast electron in overdense plasmas is of key importance in high energy density physics. However, it is challenging to diagnose the fast electron transport in experiments. In this article, we study coherent transition radiation (CTR) generated by fast electrons on the back surface of the target by using 2D and 3D first-principle particle-in-cell (PIC) simulations. In our simulations, aluminium target of 2.7 g/cc is simulated in two different situations by using a newly developed high order implicit PIC code. Comparing realistic simulations containing collision and ionization effects, artificial simulations without taking collision and ionization effects into account significantly underestimate the energy loss of electron beam when transporting in the target, which fail to describe the complete characteristics of CTR produced by electron beam on the back surface of the target. Realistic simulations indicate the diameter of CTR increases when the thickness of the target is increased. This is attributed to synergetic energy losses of high flux fast electrons due to Ohm heatings and colliding drags, which appear quite significant even when the thickness of the solid target only differs by micrometers. Especially, when the diagnosing position is fixed, we find that the intensity distribution of the CTR is also a function of time, with the diameter increased with time. As the diameter of CTR is related to the speed of electrons passing through the back surface of the target, our finding may be used as a new tool to diagnose the electron energy spectra near the surface of solid density plasmas.

##### 2.Suppressing stimulated Raman side-scattering by vector light

**Authors:**Xiaobao Jia, Qing Jia, Rui Yan, Jian Zheng

**Abstract:** Recently, the verification of stimulated Raman side-scattering (SRSS) in different laser inertial confinement fusion ignition schemes poses an underlying risk of SRSS on ignition. In this paper, we propose a method to use the non-uniform polarization nature of vector light to suppress SRSS and give an additional threshold condition determined by the parameter of vector light. For SRSS at 90 degrees, where the scattered electromagnetic wave travels perpendicular to the density profile, the polarization variation of the pump will change the wave vector of scattered light, thereby reducing the growth length and preventing the scattered electromagnetic wave from growing. This suppressive scheme is verified through three-dimensional particle-in-cell simulations. Our illustrative simulation results demonstrate that for linearly polarized Gaussian light, the SRSS signal occurs in the 90-degree direction fiercely. At the same time, for the vector light, there is few SRSS signal even if the condition dramatically exceeds the threshold. Furthermore, we discuss the impact of vector light on stimulated Raman and Brillouin backscattering, and two-plasma decay.

##### 1.Steady regime of radiation pressure acceleration with foil thickness adjustable within micrometers under 10-100 PW laser

**Authors:**Meng Liu, Wei-Min Wang, Yu-Tong Li

**Abstract:** Quasi-monoenergetic GeV-scale protons are predicted to efficiently generate via radiation pressure acceleration (RPA) when the foil thickness is matched with the laser intensity, e.g., $L_{mat}$ at several nm to 100 nm with $10^{19}-10^{22} \rm ~W cm^{-2}$ available in laboratory. However, non-monoenergetic protons with much lower energies than prediction were usually observed in RPA experiments, because of too small foil thickness which is hard to bear insufficient laser contrast and foil surface roughness. Besides the technical problems, we here find that there is an upper-limit thickness $L_{up}$ derived from the requirement that the laser energy density should dominate over the ion source, and $L_{up}$ is lower than $ L_{mat}$ with the intensity below $10^{22} \rm~ W cm^{-2}$, which causes inefficient or unsteady RPA. As the intensity is enhanced to $\geq 10^{23} \rm ~W cm^{-2}$ provided by 10-100 PW laser facilities, $L_{up}$ can significantly exceed $L_{mat}$ and therefore RPA becomes efficient. In this regime, $L_{mat}$ acts as a lower-limit thickness for efficient RPA, so the matching thickness can be extended to a continuous range from $L_{mat}$ to $L_{up}$; the range can reach micrometers, within which foil thickness is adjustable. This makes RPA steady and meanwhile the above technical problems can be overcome. Particle-in-cell simulation shows that multi-GeV quasi-monoenergetic proton beams can be steadily generated and the fluctuation of the energy peaks and the energy conversation efficiency remains stable although the thickness is taken in a larger range with increasing intensity. This work predicts that near future RPA experiments with 10-100 PW facilities will enter a new regime with the adjustable and large-range foil thickness for steady acceleration.

##### 2.Enhancement of Fusion Reactivity under Non-Maxwellian Distributions: Effects of Drift-Ring-Beam, Slowing-Down, and Kappa Super-Thermal Distributions

**Authors:**Haozhe Kong, Huasheng Xie, Bing Liu, Muzhi Tan, Di Luo, Zhi Li, Jizhong Sun

**Abstract:** Non-Maxwellian distributions of particles are commonly observed in fusion studies, especially for magnetic confinement fusion plasmas. The particle distribution has a direct effect on fusion reactivity, which is the focus of this study. We investigate the effects of three types of non-Maxwellian distributions, namely drift-ring-beam, slowing-down, and kappa super-thermal distributions, on the fusion reactivities of D-T (Deuterium-Trillium) and p-B11 (proton-Boron) using a newly developed program, where the enhancement of fusion reactivity relative to the Maxwellian distribution is computed while keeping the total kinetic energy constant. The calculation results show that for the temperature ranges of interest to us, namely 5-50 keV for D-T and 100-500 keV for p-B11, these non-Maxwellian distributions can enhance the fusion reactivities. In the case of the drift-ring-beam distribution, the enhancement factors for both reactions are affected by the perpendicular ring beam velocity, leading to decreased enhancement in low temperature range and increased enhancement in high temperature range. However, this effect is favorable for p-B11 fusion reaction and unfavorable for D-T fusion reaction. In the slowing-down distribution, the birth speed plays a crucial role in both reactions, and increasing birth speed leads to a shift in the enhancement ranges towards lower temperatures, which is beneficial for both reactions. Finally, the kappa super-thermal distribution results in a relatively large enhancement in the low temperature range with a small high energy power-law index {\kappa}. Overall, this study provides insight into the effects of non-Maxwellian distributions on fusion reactivity and highlights potential opportunities for enhancing fusion efficiency.

##### 1.Global simulations of kinetic-magnetohydrodynamic processes with energetic electrons in tokamak plasmas

**Authors:**Jian Bao, Wenlu Zhang, Ding Li, Zhihong Lin, Zhiyong Qiu, Wei Chen, Xiang Zhu, Junyi Cheng, Chao Dong, Jintao Cao

**Abstract:** The energetic electrons (EEs) generated through auxiliary heating have been found to destabilize various Alfven eigenmodes (AEs) in recent experiments, which in turn lead to the EE transport and degrade the plasma energy confinement. In this work, we propose a global fluid-kinetic hybrid model for studying corresponding kinetic-magnetohydrodynamic (MHD) processes by coupling the drift-kinetic EEs to the Landau-fluid model of bulk plasmas in a non-perturbative manner. The numerical capability of Landau-fluid bulk plasmas is obtained based on a well-benchmarked eigenvalue code MAS [Multiscale Analysis of plasma Stabilities, J. Bao et al. Nucl. Fusion accepted 2023], and the EE responses to the electromagnetic fluctuations are analytically derived, which not only contribute to the MHD interchange drive and parallel current but also lead to the newly kinetic particle compression with the precessional drift resonance in the leading order. The hybrid model is casted into a nonlinear eigenvalue matrix equation and solved iteratively using Newton's method. By calibrating the EE precession frequency against the particle equation of motion in general geometry and applying more realistic trapped particle distribution in the poloidal plane, MAS simulations of EE-driven beta-induced Alfven eigenmodes (e-BAE) show excellent agreements with gyrokinetic particle-in-cell simulations, and the non-perturbative effects of EEs on e-BAE mode structure, growth rate and damping rate are demonstrated. With these efforts, the upgraded MAS greatly improves the computation efficiency for plasma problems related to deeply-trapped EEs, which is superior than initial-value simulations restricted by the stringent electron Courant condition regarding to the practical application of fast linear analysis.

##### 2.Development of the Self-Modulation Instability of a Relativistic Proton Bunch in Plasma

**Authors:**L. Verra
AWAKE Collaboration, S. Wyler
AWAKE Collaboration, T. Nechaeva
AWAKE Collaboration, J. Pucek
AWAKE Collaboration, V. Bencini
AWAKE Collaboration, M. Bergamaschi
AWAKE Collaboration, L. Ranc
AWAKE Collaboration, G. Zevi Della Porta
AWAKE Collaboration, E. Gschwendtner
AWAKE Collaboration, P. Muggli
AWAKE Collaboration

**Abstract:** Self-modulation is a beam-plasma instability that is useful to drive large-amplitude wakefields with bunches much longer than the plasma skin depth. We present experimental results showing that, when increasing the ratio between the initial transverse size of the bunch and the plasma skin depth, the instability occurs later along the bunch, or not at all, over a fixed plasma length, because the amplitude of the initial wakefields decreases. We show cases for which self-modulation does not develop and we introduce a simple model discussing the conditions for which it would not occur after any plasma length. Changing bunch size and plasma electron density also changes the growth rate of the instability. We discuss the impact of these results on the design of a particle accelerator based on the self-modulation instability seeded by a relativistic ionization front, such as the future upgrade of the AWAKE experiment.

##### 3.Hybrid-VPIC: an Open-Source Kinetic/Fluid Hybrid Particle-in-Cell Code

**Authors:**Ari Le, Adam Stanier, Lin Yin, Blake Wetherton, Brett Keenan, Brian Albright

**Abstract:** Hybrid-VPIC is an extension of the open-source high-performance particle-in-cell (PIC) code VPIC incorporating hybrid kinetic ion/fluid electron solvers. This paper describes the models that are available in the code and gives an overview of applications of the code to space and laboratory plasma physics problems. Particular choices in how the hybrid solvers were implemented are documented for reference by users. A few solutions for handling numerical complications particular to hybrid codes are also described. Special emphasis is given to the computationally taxing problem of modeling mix in collisional high-energy-density regimes, for which more accurate electron fluid transport coefficients have been implemented for the first time in a hybrid PIC code.

##### 1.Response of a dusty plasma system to external charge perturbations}

**Authors:**Hitendra Sarkar, Madhurjya P. Bora

**Abstract:** The excitation of nonlinear wave structures in a dusty plasma caused by a moving external charge perturbation is examined in this work, which uses a 1-D flux corrected transport simulation. The plasma responds uniquely to different nature of the moving charge, depending on which, for small amplitude perturbations, pinned envelope solitons are generated and electrostatic dispersive ion-acoustic shock waves are formed for a large amplitude perturbation. The presence of dust particles is found to suppress the formation of dispersive shocks at low velocity of the external charge debris. The results are also investigated theoretically as a solution to the generalized Gross-Piteavskii equation, which broadly supports the simulation results.

##### 2.A preliminary analysis for efficient laser wakefield acceleration

**Authors:**Gaetano Fiore

**Abstract:** We propose a preliminary analytical procedure in 4 steps (based on an improved fully relativistic plane hydrodynamic model) to tailor the initial density of a cold diluted plasma to the laser pulse profile so as to control wave-breaking (WB) of the plasma wave and maximize the acceleration of small bunches of electrons self-injected by the first WB at the density down-ramp.

##### 1.Numerical study of Weibel instability driven by anisotropic electron temperature in collisionless plasmas

**Authors:**A. Sladkov, A. Korzhimanov

**Abstract:** We numerically investigate the process of generating magnetic fields from temperature anisotropy of electrons in collisionless initially uniform plasmas. We use a fully kinetic modeling and compare it against a hybrid modeling which treats ions kinetically and use ten-moment fluid model for electrons. The results of the one-to-one comparison show a good agreement in terms of the maximal magnitude of the self-generated magnetic field and similar trends during the non-linear stage of the instability. Additionally, we performed hybrid modelling of the instability without resolving electron spatial scales. In this case the results are only qualitatively the same however it shows that hydrodynamical approach can be used to some extent for the simulation of the Weibel instability in large-scale systems, including astrophysical environments and laser-produced plasmas.

##### 2.How accurate are flux-tube (local) gyrokinetic codes in modeling energetic particle effects on core turbulence?

**Authors:**A. Di Siena, T. Hayward-Schneider, P. Mantica, J. Citrin, F. Vannini, A. Bottino, T. Goerler, E. Poli, R. Bilato, O. Sauter, F. Jenko

**Abstract:** Flux-tube gyrokinetic codes are widely used to simulate drift-wave turbulence in magnetic confinement devices. While a large number of studies show that flux-tube codes provide an excellent approximation for turbulent transport in medium-large devices, it still needs to be determined whether they are sufficient for modeling supra-thermal particle effects on core turbulence. This is called into question given the large temperature of energetic particles (EPs), which makes them hardly confined on a single flux-surface, but also due to the radially broad mode structure of energetic-particle-driven modes. The primary focus of this manuscript is to assess the range of validity of flux-tube codes in modeling fast ion effects by comparing radially global turbulence simulations with flux-tube results at different radial locations for realistic JET parameters using the gyrokinetic code GENE. To extend our study to a broad range of different plasma scenarios, this comparison is made for four different plasma regimes, which differ only by the profile of the ratio between the plasma kinetic and magnetic pressure. The latter is artificially rescaled to address the electrostatic limit and regimes with marginally stable, weakly unstable and strongly unstable fast ion modes. These energetic-particle-driven modes is identified as an AITG/KBAE via linear ORB5 and LIGKA simulations. It is found that the local flux-tube simulations can recover well the global results only in the electrostatic and marginally stable cases. When the AITG/KBAE becomes linearly unstable, the local approximation fails to correctly model the radially broad fast ion mode structure and the consequent global zonal patterns. According to this study, global turbulence simulations are likely required in regimes with linearly unstable AITG/KBAEs. In conditions with different fast ion-driven modes, these results might change.

##### 3.Branching of high-current relativistic electron beam in porous materials

**Authors:**K. Jiang, T. W. Huang, R. Li, M. Y. Yu, H. B. Zhuo, S. Z. Wu, C. T. Zhou, S. C. Ruan

**Abstract:** Propagation of high-current relativistic electron beam (REB) in plasma is relevant to many high-energy astrophysical phenomena as well as applications based on high-intensity lasers and charged-particle beams. Here we report a new regime of beam-plasma interaction arising from REB propagation in medium with fine structures. In this regime, the REB cascades into thin branches with local density hundred times the initial value and deposits its energy two orders of magnitude more efficiently than that in homogeneous plasma, where REB branching does not occur, of similar average density. Such beam branching can be attributed to successive weak scatterings of the beam electrons by the unevenly distributed magnetic fields induced by the local return currents in the skeletons of the porous medium. Results from a model for the excitation conditions and location of the first branching point with respect to the medium and beam parameters agree well with that from pore-resolved particle-in-cell simulations.

##### 4.A reaction mechanism for oxygen plasmas

**Authors:**Tiago C Dias, Chloé Fromentin, Luís L Alves, Antonio Tejero-del-Caz, Tiago Silva, Vasco Guerra

**Abstract:** This work presents a reaction mechanism for oxygen plasmas, i.e. a set of reactions and corresponding rate coefficients that are validated against benchmark experiments. The kinetic scheme is validated in a DC glow discharge for gas pressures of 0.2-10 Torr and currents of 10-40 mA, using the 0D LisbOn KInetics (LoKI) simulation tool and available experimental data. The comparison comprises not only the densities of the main species in the discharge - $\mathrm{O_2(X^3\Sigma_g^-)}$, $\mathrm{O_2(a^1\Delta_g)}$, $\mathrm{O_2(b^1\Sigma_g^+)}$ and $\mathrm{O(^3P)}$ - but also the self-consistent calculation of the reduced electric field and the gas temperature. The main processes involved in the creation and destruction of these species are identified. Moreover, the results show that the oxygen atoms play a dominant role in gas heating, via recombination at the wall and quenching of $\mathrm{O_2(X^3\Sigma_g^-,v)}$ vibrations and $\mathrm{O_2}$ electronically-excited states. It is argued that the development and validation of kinetic schemes for plasma chemistry should adopt a paradigm based on the comparison against standard validation tests, as it is done in electron swarm validation of cross sections.

##### 1.Quasilinear theory of Brillouin resonances in rotating magnetized plasmas

**Authors:**J. -M. Rax, R. Gueroult, N. J. Fisch

**Abstract:** Both spin and orbital angular momentum can be exchanged between a rotating wave and a rotating magnetized plasma. Through resonances the spin and orbital angular momentum of the wave can be coupled to both the cyclotron rotation and the drift rotation of the particles. It is however shown that the Landau and cyclotron resonance conditions which classically describe resonant energy-momentum exchange between waves and particles are no longer valid in a rotating magnetized plasma column. In this case a new resonance condition which involves a resonant matching between the wave frequency, the cyclotron frequency modified by inertial effects and the harmonics of the guiding center rotation is identified. A new quasilinear equation describing orbital and spin angular momentum exchanges through these new Brillouin resonances is then derived, and used to expose the wave driven radial current responsible for angular momentum absorption.

##### 1.Proton acceleration with intense twisted laser light

**Authors:**Camilla Willim, Jorge Vieira, Victor Malka, Luís O. Silva

**Abstract:** An efficient approach that considers a high-intensity twisted laser of moderate energy (few J) is proposed to generate collimated proton bunches with multi-10-MeV energies from a double-layer hydrogen target. Three-dimensional particle-in-cell simulations demonstrate the formation of a highly collimated and energetic ($\sim 40$ MeV) proton bunch, whose divergence is $\sim 6.5$ times smaller compared to the proton bunch driven by a Gaussian laser containing the same energy. Supported by theoretical modeling of relativistic self-focusing in near-critical plasma, we establish a regime that allows for consistent acceleration of high-energetic proton bunches with low divergence under experimentally feasible conditions for twisted drivers.

##### 2.Statistics of Pressure Fluctuations in Turbulent Kinetic Plasmas

**Authors:**Subash Adhikari, William H. Matthaeus, Tulasi N. Parashar, Michael A. Shay, Paul A. Cassak

**Abstract:** In this study we explore the statistics of pressure fluctuations in kinetic collisionless turbulence. A 2.5D kinetic particle-in-cell (PIC) simulation of decaying turbulence is used to investigate pressure balance via the evolution of thermal and magnetic pressure in a plasma with beta of order unity. We also discuss the behavior of thermal, magnetic and total pressure structure functions and their corresponding wavenumber spectra. The total pressure spectrum exhibits a slope of -7/3 extending for about a decade in the ion-inertial range. In contrast, shallower -5/3 spectra are characteristic of the magnetic pressure and thermal pressure. The steeper total pressure spectrum is a consequence of cancellation caused by density-magnetic field magnitude anticorrelation. Further, we evaluate higher order total pressure structure functions in an effort to discuss intermittency and compare the power exponents with higher order structure functions of velocity and magnetic fluctuations. Finally, applications to astrophysical systems are also discussed.

##### 3.Modelling of the driver transverse profile for laser wakefield electron acceleration at APOLLON Research Facility

**Authors:**Ioaquin Moulanier, Lewis Dickson, Charles Ballage, Ovidiu Vasilovici, Aubin Gremaud, Sandrine Dobosz Dufrenoy, Nicolas Delerue, Lorenzo Bernardi, Ali Mahjoub, Antoine Cauchois, Arnd Specka, Francesco Massimo, Gilles Maynard, Brigitte Cros

**Abstract:** The quality of electron bunches accelerated by laser wakefields is highly dependant on the temporal and spatial features of the laser driver. Analysis of experiments performed at APOLLON PW-class laser facility shows that spatial instabilities of the focal spot, such as shot-to-shot pointing fluctuations or asymmetry of the transverse fluence, lead to charge and energy degradation of the accelerated electron bunch. It is shown that PIC simulations can reproduce experimental results with a significantly higher accuracy when the measured laser asymmetries are included in the simulated laser's transverse profile, compared to simulations with ideal, symmetric laser profile. A method based on a modified Gerchberg-Saxton iterative algorithm is used to retrieve the laser electric field from fluence measurements in vacuum in the focal volume, and accurately reproduce experimental results using PIC simulations, leading to simulated electron spectra in close agreement with experimental results, for the accelerated charge, energy distribution and pointing of the electron beam at the exit of the plasma.

##### 1.Bounce-averaged drifts: Equivalent definitions, numerical implementations, and example cases

**Authors:**R. J. J. Mackenbach, J. M. Duff, M. J. Gerard, J. H. E. Proll, P. Helander, C. C. Hegna

**Abstract:** In this article we provide various analytical and numerical methods for calculating the average drift of magnetically trapped particles across field lines in complex geometries, and we compare these methods against each other. To evaluate bounce-integrals, we introduce a generalisation of the trapezoidal rule which is able to circumvent integrable singularities. We contrast this method with more standard quadrature methods in a parabolic magnetic well and find that the computational cost is significantly lower for the trapezoidal method, though at the cost of accuracy. With numerical routines in place, we next investigate conditions on particles which cross the computational boundary, and we find that important differences arise for particles affected by this boundary, which can depend on the specific implementation of the calculation. Finally, we investigate the bounce-averaged drifts in the optimized stellarator NCSX. From investigating the drifts, one can readily deduce important properties, such as what subset of particles can drive trapped-particle modes, and in what regions radial drifts are most deleterious to the stability of such modes.

##### 2.Comments on "Volume ignition of mixed fuel" by H. Ruhl and G. Korn (Marvel Fusion, Munich)

**Authors:**Karl Lackner, Rainer Burhenn, Sina Fietz, Alexander von Müller

**Abstract:** In the most recent note on Marvel Fusion's concept for a laser driven pB reactor without compression, Ruhl and Korn consider the volumetric energy balance of fusion reactions vs. bremsstrahlung losses in a mixed fuel (DT and pB) environment and claim the satisfaction of this necessary "ideal ignition" condition. Their results are based, however, on improper assumptions about the deposition of fusion energy in the plasma. Correcting for them, we show that the quoted composition of their fuel (a solid boron composite, binding high concentrations of D, T and p) would actually preclude ignition due to the high bremsstrahlung losses associated with the presence of boron. To facilitate ignition, Ruhl and Korn also consider the reduction of the bremsstrahlung losses by confining the radiation in the optically thin fuel region by high Z walls. They suggest to preload this region with radiation so that the radiation temperature equals approximately that of the plasma constituents $T_{r} \approx T_{e} \approx T_{i}$. We show that in this set-up the radiation energy - neglected in these considerations - would, however, vastly exceed the thermal energy of the plasma and actually dominate the ignition energy requirements.

##### 1.Estimating the properties of single positive air streamers from measurable parameters

**Authors:**Dennis Bouwman, Hani Francisco, Ute Ebert

**Abstract:** We develop an axial model for single steadily propagating positive streamers in air. It uses observable parameters to estimate quantities that are difficult to measure. More specifically, for given velocity, radius, length and applied background field, our model approximates the ionization degree, the maximal electric field, the channel electric field, and the width of the charge layer. These parameters determine the primary excitations of molecules and the internal currents. We do this by first analytically approximating the electron dynamics in different regions of a uniformly-translating streamer head, then we match the solutions between the different regions and finally we use conservation laws to determine unknown quantities. We find good agreement with numerical simulations for a range streamer lengths and background electric fields, even if they do not propagate in a steady manner. Therefore quantities that are difficult to access experimentally can be estimated from easily measurable quantities and our approximations. The theoretical approximations also form a stepping stone towards efficient axial multi-streamer models.

##### 2.The STAG Code: A Fully Relativistic Super Transition Array Calculation Using Green's Functions

**Authors:**Nathanael Gill, Christopher Fontes, Charles Starrett

**Abstract:** Calculating opacities for a wide range of plasma conditions (i.e. temperature, density, element) requires detailed knowledge of the plasma configuration space and electronic structure. For plasmas composed of heavier elements, relativistic effects are important in both the electronic structure and the details of opacity spectra. We extend our previously described superconfiguration and super transition array capabilities [N. M. Gill et al., JPB, 56, 015001 (2023)] to include a fully relativistic formalism. The use of hybrid bound-continuum supershells in our superconfigurations demonstrates the importance of a consistent treatment of bound and continuum electrons in dense plasma opacities, and we expand the discussion of these consequences to include issues associated with equation of state and electron correlations between bound and continuum electrons.

##### 1.Deep Learning assisted microwave-plasma interaction based technique for plasma density estimation

**Authors:**Pratik Ghosh, Bhaskar Chaudhury, Shishir Purohit, Vishv Joshi, Ashray Kothari

**Abstract:** The electron density is a key parameter to characterize any plasma. Most of the plasma applications and research in the area of low-temperature plasmas (LTPs) is based on plasma density and plasma temperature. The conventional methods for electron density measurements offer axial and radial profiles for any given linear LTP device. These methods have major disadvantages of operational range (not very wide), cumbersome instrumentation, and complicated data analysis procedures. To address such practical concerns, the article proposes a novel machine learning (ML) assisted microwave-plasma interaction based strategy which is capable enough to determine the electron density profile within the plasma. The electric field pattern due to microwave scattering is measured to estimate the density profile. The proof of concept is tested for a simulated training data set comprising a low-temperature, unmagnetized, collisional plasma. Different types of Gaussian-shaped density profiles, in the range $10^{16}-10^{19}m^{-3}$, addressing a range of experimental configurations have been considered in our study. The results obtained show promising performance in estimating the 2D radial profile of the density for the given linear plasma device. The performance of the proposed deep learning based approach has been evaluated using three metrics- SSIM, RMSLE and MAPE. The favourable performance affirms the potential of the proposed ML based approach in plasma diagnostics.

##### 2.Effect of non-local transport of hot electrons on the laser-target ablation

**Authors:**Z. H. Chen, X. H. Yang, G. B. Zhang, Y. Y. Ma, H. Xu, S. X. Luan, J. Zhang

**Abstract:** The non-local heat transport of hot electrons during high-intensity lasers interaction with plasmas can preheat the fuel and limit the heat flow in inertial confinement fusion. It increases the entropy of the fuel and decreases the final compression. In this paper, the non-local electron transport model that is based on the improved SNB algorithm has been embedded into the radiation hydrodynamic code and is benchmarked with two classical non-local transport cases. Then we studied a 2$\omega$ laser ablating a CH target by using the non-local module. It is found that the non-local effect becomes significant when the laser intensity is above $1\times 10^{14} \mathrm{W/cm^{2}} $. The mass ablation rate from the SNB model is increased compared to that of the flux-limited model due to the lower coronal plasma temperature. This non-local model has a better agreement with the experimental results compared to that of the flux-limited model. The non-local transport is strongly dependent on the laser frequency, and the thresholds that the non-local transport should be considered are obtained for lasers of different frequencies. The appropriate flux-limiters that should be employed in the flux-limited model for different lasers are also presented. The results here should have a good reference for the laser-target ablation applications.

##### 1.Stopping power of high-density alpha-particle clusters in warm dense deuterium-tritium fuels

**Authors:**Z. P. Fu, Z. W. Zhang, K. Lin, D. Wu, J. Zhang

**Abstract:** The state of burning plasma had been achieved in inertial confinement fusion (ICF), which was regarded as a great milestone for high-gain laser fusion energy. In the burning plasma, alpha particles incident on the cryogenic (warm dense) fuels cannot be simply regarded as single particles, and the new physics brought about by the density effects of alpha particles should be considered. In this work, the collective interaction between them has been considered, namely the effect of the superposition of wake waves. The stopping power of alpha-particle clusters, i.e. the rate of energy loss per unit distance traveled has been calculated using both analytical and simulation approaches. In theory, we obtain the stopping power of alpha clusters in cryogenic (warm dense) fuel by the dielectric function method, which illustrates the importance of the effective interaction between particles. Simulation results using the LAPINS code show that the collective stopping power of the alpha cluster is indeed increased via coherent superposition of excitation fields (the excitation of high-amplitude wake waves). However, the comparison between simulation and theoretical results also illustrates a coherent-decoherent transition of the stopping power of the cluster. The initial conditions with various sizes and densities of the alpha clusters have been considered to verify the condition of decoherence transition. Our work provides a theoretical description of the transport properties of high-density alpha particles in warm dense cryogenic fuel and might give some theoretical guidance for the design of actual fusion processes.

##### 1.A strategy to identify breakdown location in MITICA test facility: results of high voltage test campaign

**Authors:**Loris Zanotto, Marco Boldrin, Giuseppe Chitarin, Mattia Dan, Tommaso Patton, Francesco Santoro, Vanni Toigo, Hiroyuki Tobari, Atsushi Kojima, Hans Decamps

**Abstract:** The Acceleration Grid Power Supply of the MITICA test facility in Padova (Italy) is currently under commissioning. The power conversion system, the DC generator, and the High Voltage equipment have been individually commissioned, whereas the integration tests are ongoing. It is a challenging process due to the unconventional application, to the variety of different electrical technologies involved and to the complexity of the interfaces. During the integrated tests of the power supplies the achievement of 700kV stable operation has been demonstrated for the first time in a Neutral Beam Injector, but an unexpected event occurred, most likely a breakdown in the HV part, which resulted in a fault of the DC generator. A subsequent test using an auxiliary power supply was performed to check the voltage withstanding capability of the HV plant, but another breakdown occurred at around 1MV. This paper describes the activity performed to identify the location of the breakdowns affecting the integrated tests. A test campaign has been devised with increased diagnostic capabilities and specific strategy conceived to trigger intentional breakdowns in specific locations and collect measurement patterns for different cases. The results of the campaign will be presented and the current understanding of the issue will be described, with a view on future tests and further improvements of diagnostics.

##### 2.Unsupervised classification of fully kinetic simulations of plasmoid instability using Self-Organizing Maps (SOMs)

**Authors:**Sophia Köhne, Elisabetta Boella, Maria Elena Innocenti

**Abstract:** The growing amount of data produced by simulations and observations of space physics processes encourages the use of methods rooted in Machine Learning for data analysis and physical discovery. We apply a clustering method based on Self-Organizing Maps (SOM) to fully kinetic simulations of plasmoid instability, with the aim of assessing its suitability as a reliable analysis tool for both simulated and observed data. We obtain clusters that map well, a posteriori, to our knowledge of the process: the clusters clearly identify the inflow region, the inner plasmoid region, the separatrices, and regions associated with plasmoid merging. SOM-specific analysis tools, such as feature maps and Unified Distance Matrix, provide one with valuable insights into both the physics at work and specific spatial regions of interest. The method appears as a promising option for the analysis of data, both from simulations and from observations, and could also potentially be used to trigger the switch to different simulation models or resolution in coupled codes for space simulations.

##### 1.Self-consistent gyrokinetic modelling of turbulent and neoclassical tungsten transport in toroidally rotating plasmas

**Authors:**Kyungtak Lim, Xavier Garbet, Yanick Sarazin, Etienne Gravier, Maxime Lesur, Guillaume Lo-Cascio, Timothe Rouyer

**Abstract:** The effect of toroidal rotation on both turbulent and neoclassical transport of tungsten (W) in tokamaks is investigated using the flux-driven, global, nonlinear 5D gyrokinetic code GYSELA. Nonlinear simulations are carried out with different levels of momentum injection that drive W to the supersonic regime, while the toroidal velocity of the main ions remains in the subsonic regime. The numerical simulations demonstrate that toroidal rotation induces centrifugal forces that cause W to accumulate in the outboard region, generating an in-out poloidal asymmetry. This asymmetry enhances neoclassical inward convection, which can lead to central accumulation of W in cases of strong plasma rotation. The core accumulation of W is mainly driven by inward neoclassical convection. However, as momentum injection continues, roto-diffusion, proportional to the radial gradient of the toroidal velocity, becomes significant and generate outward turbulent flux in the case of ion temperature gradient (ITG) turbulence. Overall, the numerical results from nonlinear GYSELA simulations are in qualitative agreement with the theoretical predictions for impurity transport, as well as experimental observations.

##### 2.Effect of triangularity on plasma turbulence and the SOL-width scaling in L-mode diverted tokamak configurations

**Authors:**Kyungtak Lim, Maurizio Giacomin, Paolo Ricci, António Coelho, Olivier Février, Davide Mancini, Davide Silvagni, Louis Stenger

**Abstract:** The effect of triangularity on tokamak boundary plasma turbulence is investigated by using global, flux-driven, three-dimensional, two-fluid simulations. The simulations show that negative triangularity stabilizes boundary plasma turbulence, and linear investigations reveal that this is due to a reduction of the magnetic curvature drive of interchange instabilities, such as the resistive ballooning mode. As a consequence, the pressure decay length $L_p$, related to the SOL power fall-off length $\lambda_q$, is found to be affected by triangularity. Leveraging considerations on the effect of triangularity on the linear growth rate and nonlinear evolution of the resistive ballooning mode, the analytical theory-based scaling law for $L_p$ in L-mode plasmas, derived by Giacomin \textit{et al.} [{Nucl. Fusion}, \href{https://doi.org/10.1088/1741-4326/abf8f6}{\textbf{61} 076002} (2021)], is extended to include the effect of triangularity. The scaling is in agreement with nonlinear simulations and a multi-machine experimental database, which include recent TCV discharges dedicated to the study of the effect of triangularity in L-mode diverted discharges. Overall, the present results highlight that negative triangularity narrows the $L_p$ and considering the effect of triangularity is important for a reliable extrapolation of $\lambda_q$ from present experiments to larger devices.