Table of contents

Three dimensional particle in cell simulations of laser wakefield acceleration require a considerable amount of resources but are necessary to have realistic predictions and to design future experiments. The planned experiments for the Apollon laser also include two stages of plasma acceleration, for a total plasma length of the order of tens of millimeters or centimeters. In this context, where traditional 3D numerical simulations would be computationally very expensive, we present the results of the application of a recently proposed envelope method, to describe the laser pulse and its interaction with the plasma without the need to resolve its high frequency oscillations. The implementation of this model in the code Smilei is described, as well as the results of benchmark simulations against standard laser simulations and applications for the design of two stage Apollon experiments.

Plasma-based deceleration could greatly improve the overall compactness of accelerator facilities. In the so-called passive plasma beam dump, collective oscillations of plasma electrons are used to absorb kinetic energy of spent high-energy electron beams. Moreover, due to the high-amplitude decelerating gradient and the low-density plasma medium, deceleration is achieved in a compact and safer way, if compared to conventional beam dumps. Adoption of this novel decelerating scheme might be critical for facilities aiming for high-energy, high-repetition-rates, as well as for transportable applications built upon plasma-based accelerator technology. However, key issues such as, for example, particle re-acceleration, need to be addressed. In this work, tailored plasma-density profiles are used to shift the defocusing phase of the beam self-driven transverse wakefield towards re-accelerated beam particles, and transversely eject them. PIC simulations are used to evaluate the total beam energy, energy deposited in the plasma, and energy transversely ejected, for each of the investigated plasma density profiles. Moreover, the average energy per ejected particle is estimated for each case. In particular, it is shown that the energy of ejected particles is affected by the rate at which the plasma wavelength decreases, since it determines the time that particles experience re-acceleration before being defocused.

Toroidal rotation is critical for fusion in tokamaks, since it stabilizes instabilities that can otherwise cause disruptions or degrade confinement. Unlike present-day devices, ITER might not have enough neutral-beam torque to easily avoid these instabilities. We must therefore understand how the plasma rotates 'intrinsically,' that is, without applied torque. Experimentally, torque-free plasmas indeed rotate, with profiles that are often non-flat and even non-monotonic. The rotation depends on many plasma parameters including collisionality and plasma current, and exhibits sudden bifurcations ('rotation reversals') at critical parameter values.

Since toroidal angular momentum is conserved in axisymmetric systems, and since experimentally inferred momentum transport is much too large to be neoclassical, theoretical work has focused on rotation drive by nondiffusive turbulent momentum fluxes. In the edge, intrinsic rotation relaxes to a steady state in which the total momentum outflux from the plasma vanishes. Ion drift orbits, scrape-off-layer flows, separatrix geometry, and turbulence intensity gradient all play a role. In the core, nondiffusive and viscous momentum fluxes balance to set the rotation gradient at each flux surface. Although many mechanisms have been proposed for the nondiffusive fluxes, most are treated in one of two distinct but related gyrokinetic formulations. In a radially local fluxtube, appropriate for ${\rho }_{\ast }\ll 1$, the lowest-order gyrokinetic formulations exhibit a symmetry that prohibits nondiffusive momentum flux for nonrotating plasmas in an up-down symmetric magnetic geometry with no ${\boldsymbol{E}}\times {\boldsymbol{B}}$ shear. Many symmetry-breaking mechanisms have been identified, but none have yet been conclusively demonstrated to drive a strong enough flux to explain commonly observed experimental rotation profiles. Radially global gyrokinetic simulations naturally include many symmetry-breaking mechanisms, and have shown cases with experimentally relevant levels of nondiffusive flux. These promising early results motivate further work to analyze, verify, and validate.

This article provides a pedagogical introduction to intrinsic rotation in axisymmetric devices. Intended for both newcomers to the topic and experienced practitioners, the article reviews a broad range of topics including experimental and theoretical results for both edge and core rotation, while maintaining a focus on the underlying concepts.

To maximize the charge of a high-energy electron beam accelerated by an ultra-intense laser pulse propagating in a subcritical plasma, the pulse length should be longer than both the plasma wavelength and the laser pulse width, which is quite different from the standard bubble regime. In addition, the laser-plasma parameters should be chosen to produce the self-trapping regime of relativistic channeling, where the diffraction divergence is balanced by the relativistic nonlinearity such that the laser beam radius is unchanged during pulse propagation in a plasma over many Rayleigh lengths. The condition for such a self-trapping regime is the same as what was empirically found in several previous simulation studies in the form of the pulse width matching condition. Here, we prove these findings for a subcritical plasma, where the total charge of high-energy electrons reaches the multi-nC level, by optimization in a 3D PIC simulation study and compare the results with an analytic theory of relativistic self-focusing. A very efficient explicitly demonstrated generation of high-charge electron beams opens a way to a high-yield production of gammas, positrons, and photonuclear particles.

Classical particle drifts are known to have substantial impacts on fluxes of particles and heat through the edge plasmas in both tokamaks and stellarators. Here we present results from the first dedicated investigation of drift effects in the W7-X stellarator. By comparing similar plasma discharges conducted with a forward- and reverse-directed magnetic field, the impacts of drifts could be isolated through the observation of up-down asymmetries in flux profiles on the divertor targets. In low-density plasmas, the radial locations of the strike lines (i.e. peaks in the target heat flux profiles) exhibited discrepancies of up to 3 cm that reversed upon magnetic field reversal. In addition, asymmetric heat loads were observed in regions of the target that are shadowed by other targets from parallel flux from the core plasma. A comparison of these asymmetric features with the footprints of key topological regions of the edge magnetic field on the divertor suggests that the main driver of the asymmetries at low density is poloidal E × B drift due to radial electric fields in the scrape-off layer and private flux region. In higher-density plasmas, upper and lower targets collected non-ambipolar currents with opposite signs that also inverted upon field reversal. Overall, in these experiments, almost all up-down asymmetry could be attributed to the field reversal and, therefore, field-dependent drifts.

The influence of ionization on the formation of a plasma channel and the propagation of a relativistic electron beam in a near-critical density hydrocarbon gas are investigated by using two-dimensional (2D) particle-in-cell (PIC) simulations. A magnetic-dipole vortex is formed and self-sustained by its magnetic field pressure inside the plasma channel when the short pulse laser energy is almost depleted. After its formation, the magnetic dipole vortex moves forward with the relativistic electron beam in the plasma channel. In a fully ionized plasma, a high density plasma barrier is usually formed ahead of the plasma channel due to the steepening density profile. Therefore, deflection of the plasma channel can easily occur during the forward movement of the magnetic dipole vortex. In contrast, the deflection of the plasma channel is suppressed by the ionization effect with hydrocarbon gas. Two main mechanisms to suppress the deflection have been found—a decrease in the plasma density steepening at the front of the plasma channel in a partly-ionized plasma, and the consumption of the electromagnetic field energy due to the ionization itself.

A vortex laser pulse is incident on a plasma with a density gradient along one transverse direction and a homogeneous density along the other one. As the laser pulse propagates in the plasma, the transverse energy distribution becomes asymmetric along the direction with the homogeneous density, which is shown from particle-in-cell simulations. We demonstrate theoretically that the asymmetric energy distribution results from the rate of plasma density change along the transverse energy flow of the vortex beam. Meanwhile, the degree of asymmetry is found to be positively related to the topological charge of the vortex beam as well as the density gradient of the plasma. Our finding provides a new approach for measuring the topological charge of a vortex beam, and also implies an available probe of the inhomogeneity of an optical medium.

The force on a test charge moving through a strongly magnetized plasma is calculated using linear response theory. Strong magnetization is found to generate a component of the force perpendicular to the velocity of the particle in the plane formed by the velocity and magnetic field vectors. This transverse force is generated by an asymmetry with respect to the velocity vector in the induced electrostatic wake potential that is associated with the action of the Lorentz force on the background plasma. The direction depends on the speed of the test charge. If it is faster than a critical speed characteristic of the sound speed, it acts to reduce the component of velocity parallel to the magnetic field and to increase the gyroradius. In contrast, if the speed is below this critical speed, it acts to increase the velocity parallel to the magnetic field and to decrease the gyroradius. Because the transverse force is perpendicular to the velocity, it does not directly influence the total energy of the test charge. Nevertheless, it significantly alters the trajectory on a timescale associated with the Coulomb collision time.

This research numerically investigates the plasma behavior during neutral gases puffing into the west end-cell of the linear plasma confinement device GAMMA 10/PDX. A multi-fluid code named 'LINDA' is developed and applied at the west end-cell of the device to explore the processes of plasma detachment and energy loss mechanism during plasma-neutral interactions. The ion heat flux limiter is newly introduced in the LINDA code. In the paper, we investigate the influence of the ion heat flux limiter in our divertor plasma models to understand how the ion heat flux limiter affects the computed plasma parameters. The upstream plasma parameters are ${n}_{{\rm{i}}}=1\times {10}^{19}\,{{\rm{m}}}^{-3},\,{T}_{{\rm{e}}}=30\,{\rm{eV}},{\rm{and}}\,{T}_{{\rm{i}}}=100\,{\rm{eV}}.$ The effect of ion heat flux limiting reduces the ion temperature and heat flux in the direction of the target plate. The ion temperature profile is shown to be similar when the heat flux limiting factor (α_i) is varied from 0.2 to 2.0. The effect of Hydrogen (H) and Argon (Ar) gas puffing has been investigated under the condition of ion heat flux limiting factors α_i = 1.0. The ion temperature is shown to be similar between Ar and without Ar puffing. On the other hand, T_e reduces remarkably for Ar puffing by enhancing the radiation cooling of Ar. The ion and electron loss are greatly enhanced for combined puffing of Ar and H. The ionization loss is found to be slightly higher and the charge-exchange loss is found to be slightly lower during the ion heat flux limiting case. These outcomes may contribute to understanding the plasma detachment processes in fusion devices.

In this paper, electromagnetic emission at the plasma frequency produced by a short laser pulse in a finite-size plasma layer with a longitudinal density modulation is studied using both analytical theory and particle-in-cell simulations. The radiation mechanism suggests that a laser pulse excites a long-lived plasma wake which, in the presence of ion density modulation with the appropriate period, generates a superluminal satellite capable of matching in phase with vacuum electromagnetic waves. It is found that such a mechanism can be used for generating tunable narrow-band (5%) multi-mJ terahertz pulses with high efficiency (>0.3%) due to ability of superluminal plasma oscillations at the cut-off frequency to diffuse through a plasma that is several times wider than the radiation wavelength.

We present synthetic spectra for light emission following charge exchange (CX) recombination for Ne-like W⁶⁴⁺ ions colliding with neutral atomic hydrogen at 100 and 500 keV/u, which is of relevance to the plasma diagnostics of the international experimental fusion device ITER now under construction. The spectra are calculated using a detailed collisional-radiative model for the W⁶³⁺ ion that includes more than 6000 singly- and doubly-excited states and accounts for major physical processes in hot fusion plasmas. The CX cross sections into excited states are computed using the classical trajectory Monte Carlo method. A comprehensive analysis of the modifications to the spectra due to CX is presented.

The emission of electrostatic Langmuir waves by collisional process, termed electrostatic bremsstrahlung emission, and the collisional damping of Langmuir waves, which can be considered as the inverse electrostatic bremsstrahlung process, are rigorously discussed. Some inaccuracies in the previous formalisms are also corrected. It is shown that the improved formulae in the case of Maxwellian particle distributions are given in forms where they satisfy Kirchhoff's law in the balanced form.

Two Ohmic H-mode discharges of the tokamak Globus-M with similar parameters and different magnetic configurations were simulated with SOLPS-ITER code. One of the discharges has two separatrices and an active low X-point—the disconnected double null (DDN) configuration. The second discharge has a connected double null configuration (CDN). The modelled plasma parameters were matched to the experimentally measured values. The scrape-off layer (SOL) width and energy loads on the divertor targets were analysed for both cases. It is demonstrated that for the Globus-M CDN configuration discharge the energy peak load at the lower outer divertor plate is approximately half of that in the case of the DDN configuration. It is also shown that the electric currents flowing from the plasma to the target plates significantly change the energy flux to the plates in both cases with respect to the flux that would be expected for the floating potential at the plates. Two types of electric currents flowing to the plates were observed. The first is a well-known thermoelectric current flowing between magnetically connected plates with different electron temperatures. This current is more pronounced in the DDN case and is strongly reduced in the CDN case, where the difference between the temperatures at the lower and upper plates is smaller. Additionally, a new second type of electric current to the plates is observed which could be called the plate closing current (PCC). These currents close radial currents in the SOL and private region. For the DDN case the PCC is comparable with the thermoelectric currents, while for CDN case the PCC is dominant.

The transient nature of magnetic reconnection dictates that it must be accompanied by rich electromagnetic wave activity, which can in turn affect the reconnection process. Interaction between Alfvén waves and reconnection has been simulated and recently observed in space. In this paper we report the first laboratory observation of a kinetic Alfvén wave (KAW) mode during reconnection in a linear device. The reconnection was measured by magnetic probes and the enhancement of light emission during reconnection was captured by a fast camera. The perpendicular wave pattern suggests it is an m = −2 mode rotating in ion diamagnetism direction. The wave data agrees with the theoretical prediction of KAW. The temporal correlation between KAW amplitude and reconnection rate indicates waves are generated by reconnection.

Scaling of the density peaking for positive magnetic shear ELMy H-mode plasmas in JT-60U has been developed. Although the density peaking generally depends on collisionality, a variation of the density peaking factor for the same collisionality exists, and the variation is different between plasmas with co-directed and ctr-directed toroidal rotation(co-V_T plasmas and ctr-V_T plasmas). The variation of the co-V_T plasmas can be explained by particle source profile. As a result of scaling, the peaking factor of the co-V_T plasmas depends on the particle source rate profile from neutral beams (NBs) as much as collisionality. The dataset of the ctr-V_T plasmas has a larger variation of the peaking factor compared to that of the co-V_T plasmas. The larger variation stems from that the peaking factor of the ctr-V_T plasmas also depends on the normalized ion temperature gradient at the edge region. As a result of scaling, the normalized ion temperature gradient influences the peaking factor as much as or a little larger than collisionality. The parameter regime of the ctr-V_T plasmas ranges from the trapped electron mode (TEM) to the ion temperature gradient mode (ITG mode). The plasmas with the positive correlation between the normalized density gradient and the normalized ion temperature gradient are dominated by the TEM. On the other hand, the plasmas with the negative correlation are dominated by the ITG mode.

We present an analysis which suggests that model selection is a critical ingredient for successful reconstruction of impurity transport coefficient profiles, D and V, from experimental data. Determining these quantities is a challenging nonlinear inverse problem. We use synthetic data to show that this problem is ill-posed, and hence D and V are not recommended for use in validation metrics unless the data analysis procedure goes to great lengths to account for the possibility that there are multiple possible solutions. In particular, inferred profiles which are very different from the true ones yield seemingly reasonable goodness-of-fit for synthetic x-ray spectrometer data. We present a Bayesian approach for inferring D and V which provides a rigorous means of selecting the level of complexity of the inferred profiles, thereby enabling successful reconstruction of the profiles.

We study the existence of steady solutions of ideal magnetofluid systems (ideal MHD and ideal Euler equations) without continuous Euclidean symmetries. The existence of such solutions can potentially allow for complex shapes in the design of confining magnetic fields. It is shown that all nontrivial magnetofluidostatic solutions are locally symmetric, although the symmetry is not necessarily an Euclidean isometry. Furthermore, magnetofluidostatic equations admit both force-free (Beltrami type) and non-force-free (with finite pressure gradients) solutions that do not exhibit invariance under translations, rotations, or their combination. Examples of smooth solutions without continuous Euclidean symmetries in bounded domains are given. Finally, the existence of square integrable solutions of the tangential boundary value problem without continuous Euclidean symmetries is proved.

The role of toroidal plasma currents for the island divertor scrape-off layer in the stellarator Wendelstein 7-X is investigated using reciprocating electric probes. Experiments show that small amounts (of a few kA) of plasma current are sufficient to significantly affect the scrape-off layer plasma conditions, whereas higher plasma currents above 10kA result in more drastic changes. This behavior is linked to the effect of the plasma current on the rotational transform profile, which can result in significant shifts of the edge magnetic islands. These shifts affect the interaction of the islands with the divertor and can eventually result in a transition from a diverted to a limited plasma configuration. The probe observations are complemented by further edge diagnostics including plasma flow measurements, divertor Langmuir probes, divertor thermography and impurity spectroscopy.

A reduced model of high-Z impurities erosion and redeposition is presented to analyze net erosion of tungsten material in divertor attached plasma conditions measured in DIII-D experiments. This reduced model is tailored to quantify the redeposition and the net erosion on high-Z material samples of sufficiently small dimensions to be considered exposed to uniform plasma conditions. For those uniform plasma conditions, the spatial distribution of redeposited high-Z impurities is well approximated by an analytical distribution characterized by a few parameters. The fraction of high-Z impurity eroding and redepositing on a material sample is then obtained by integrating this distribution across the material sample. The ratio of net erosion rates of tungsten measured experimentally from tungsten samples of different sizes exposed to the same attached plasma conditions are well reproduced with this reduced model. It is shown that uncertainties induced by radially non-uniform plasma conditions in experiments can be significantly reduced by exposing samples to high density divertor plasma. Several enhanced experimental setups are proposed to measure and compare net erosion rates from samples of various areas during a single plasma experiment.

An experimental study of laser driven electron acceleration in N₂ and N₂-He mixed gas-jet targets using laser pulses with durations of ∼60–70 fs is presented. Generation of relativistic electron beams with quasi-thermal spectra was observed at a threshold plasma density of ∼1.6 × 10¹⁸ cm⁻³ in the case of pure N₂. The threshold density was found to increase with increasing doping concentrations of He. At an optimum fraction of 50% of He in N_2, generation of quasi-monoenergetic electron beams was observed at a comparatively higher threshold density of ∼2 × 10¹⁸ cm⁻³, with an average peak energy of ∼168 MeV, average energy spread of ∼21%, and average total beam charge of ∼220 pC. The electron acceleration could be attributed to direct laser acceleration as well as the hybrid mechanism. The observation of an optimum fraction of He in N₂ (in turn threshold plasma density) for comparatively better quality electron beam generation can be understood in terms of the plasma density dependent variation in the dephasing rate of electrons with respect to the transverse oscillating laser field. Results are also supported by 2D particle-in-cell simulations performed using the code EPOCH.

Tungsten (W) spectroscopy is known to be a useful tool for quantifying W fluxes in tokamaks. We aim to analyze how background plasma parameters influence the W spectral-line shape measured in the divertor and scrape-off layer and what information could be retrieved from such an analysis. To that end, a Monte Carlo model is developed to simulate the line shape of the 400.9 nm W I line emitted by physically sputtered W ions from plasma facing components. The influence of background plasma parameters (ion and electron temperature) and geometrical effects (detector positioning with respect to the eroded surface) are investigated. The effect of Zeeman splitting on the spectral line-shape is also explored. A set of requirements for the experimental set-up needed to measure the analyzed spectral line features with line peak shifts of the order of 10⁻²Å and peak widths in the range from 10⁻¹Å to 10⁻²Å are proposed. These requirements are shown to be experimentally accessible, through the installation of specific high-resolution spectrometers not typically used on magnetic fusion devices.

The physics of divertor detachment is determined by divertor power, particle and momentum balance. This work provides a novel analysis technique of the Balmer line series to obtain a full particle/power balance measurement of the divertor. This supplies new information to understand what controls the divertor target ion flux during detachment. Atomic deuterium excitation emission is separated from recombination quantitatively using Balmer series line ratios. This enables analysing those two components individually, providing ionisation/recombination source/sinks and hydrogenic power loss measurements. Probabilistic Monte Carlo techniques were employed to obtain full error propagation—eventually resulting in probability density functions for each output variable. Both local and overall particle and power balance in the divertor are then obtained. These techniques and their assumptions have been verified by comparing the analysed synthetic diagnostic 'measurements' obtained from SOLPS simulation results for the same discharge. Power/particle balance measurements have been obtained during attached and detached conditions on the TCV tokamak.

The RF properties of the four ion cyclotron range of frequencies (ICRF) antennas in the ASDEX Upgrade tokamak are characterized in H-mode magnetically perturbed 3D discharges. An n = 2 magnetic perturbation (MP) field is applied and rigidly rotated, which allows diagnosing the separatrix displacement and consequent coupling change. We find the antenna loading resistance to be coherently modified by the resulting non-axisymmetric plasma equilibria, thus becoming a function of the applied MP field poloidal mode spectra. We perform a detailed statistical analysis, which correlates the change in loading resistance to the fast wave R-cutoff layer movements. From it, a 1D scaling is derived that differs from previous studies evaluated in pure axisymmetric plasma conditions. This experimentally derived scaling is used to predict the average loading resistance change of the ITER ICRF antenna under applied MPs. ICRF coupling simulations using measured 1D density profiles are performed with the RAPLICASOL code, in order to investigate the predictive capabilities of numerical state of the art tools. We find that both 1D conventional scaling laws and 1D numerical simulations fail to capture the 3D physics, and can substantially overestimate the measured loading resistance change up to a factor of ∼3.