The afterglow emission from gamma-ray bursts (GRBs) is usually interpreted as synchrotron radiation from electrons accelerated at the GRB external shock that propagates with relativistic velocities into the magnetized interstellar medium. By means of multi-dimensional particle-in-cell simulations, we investigate the acceleration performance of weakly magnetized relativistic shocks, in the magnetization range 0 ? 10?1. The pre-shock magnetic field is orthogonal to the flow, as generically expected for relativistic shocks. We find that relativistic perpendicular shocks propagating in electron-positron plasmas are efficient particle accelerators if the magnetization is ? 10?3. For electron-ion plasmas, the transition to efficient acceleration occurs for ? 3 ? 10?5. Here, the acceleration process proceeds similarly for the two species, since the electrons enter the shock nearly in equipartition with the ions, as a result of strong pre-heating in the self-generated upstream turbulence. In both electron-positron and electron-ion shocks, we find that the maximum energy of the accelerated particles scales in time as ?maxt 1/2. This scaling is shallower than the so-called (and commonly assumed) Bohm limit ?maxt, and it naturally results from the small-scale nature of the Weibel turbulence generated in the shock layer. In magnetized plasmas, the energy of the accelerated particles increases until it reaches a saturation value ?sat/?0 mic 2 ~ ??1/4, where ?0 mic 2 is the mean energy per particle in the upstream bulk flow. Further energization is prevented by the fact that the self-generated turbulence is confined within a finite region of thickness ??1/2 around the shock. Our results can provide physically grounded inputs for models of non-thermal emission from a variety of astrophysical sources, with particular relevance to GRB afterglows.

https://iopscience.iop.org/article/10.1088/0004-637X/771/1/54/pdf

The maximum energy of accelerated particles in relativistic collisionless shocks

Experimental investigations carried out in the ASDEX Upgrade tokamak under various conditions demonstrate that the ion heat flux at the plasma edge plays a key role in the L–H transition physics, while the electron heat flux does not seem to play any role. This is due to the fact that the ion heat flux governs the radial electric field well induced by the main ions which is responsible for the turbulence stabilization causing the L–H transition. The experiments have been carried out in the low density branch of the power threshold where the electron and ion heat channels can be well separated. In plasmas heated by electron heating, the edge ion heat flux has been increased to reach the L–H transition by using separately three actuators: heating power, density and plasma current. In addition, the key role of the edge ion heating has been confirmed in experiments taking advantage of the direct ion heating provided by neutral beam injection. The role of the ion heat flux explains the non-monotonic density dependence of the L–H threshold power. Based on these results, a formula for the density of the threshold minimum has been developed, which also describes well the values found in tokamaks of various size. For ITER it predicts a value which is close to the density presently foreseen to enter the H-mode and indicates that operation at half field and current would benefit from a very significantly lower density minimum and correspondingly low threshold power.

/pdf/experimental-evidence-for-the-key-role-of-the-ion-heat-37lfjfyu6w.pdf

Experimental evidence for the key role of the ion heat channel in the physics of the L–H transition

The current understanding of magnetohydrodynamic (MHD) turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheetlike structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale $\ensuremath{\lambda}\ensuremath{\sim}L{S}_{L}^{\ensuremath{-}4/7}$, where ${S}_{L}$ is the outer-scale ($L$) Lundquist number and $\ensuremath{\lambda}$ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the subinertial, reconnection interval of MHD turbulence, with the estimated scaling of the Fourier energy spectrum $E({k}_{\ensuremath{\perp}})\ensuremath{\propto}{k}_{\ensuremath{\perp}}^{\ensuremath{-}5/2}$, where ${k}_{\ensuremath{\perp}}$ is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas ($Pm$), where the reconnection scale is found to be $\ensuremath{\lambda}/L\ensuremath{\sim}{S}_{L}^{\ensuremath{-}4/7}P{m}^{\ensuremath{-}2/7}$.

Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence

An overview of the H-mode threshold power in ASDEX Upgrade which addresses the impact of the tungsten versus graphite wall, the dependences upon plasma current and density, as well as the influence of the plasma ion mass is given. Results on the H–L back transition are also presented. Dedicated L–H transition studies with electron heating at low density, which enable a complete separation of the electron and ion channels, reveal that the ion heat flux is a key parameter in the L–H transition physics mechanism through the main ion pressure gradient which is itself the main contribution to the radial electric field and the induced flow shearing at the edge. The electron channel does not play any role. The 3D magnetic field perturbations used to mitigate the edge-localized modes are found to also influence the L–H transition and to increase the power threshold. This effect is caused by a flattening of the edge pressure gradient in the presence of the 3D fields such that the L–H transitions with and without perturbations occur at the same value of the radial electric field well, but at different heating powers.

/pdf/survey-of-the-h-mode-power-threshold-and-transition-physics-2204fbpr7m.pdf

Survey of the H-mode power threshold and transition physics studies in ASDEX Upgrade

The achievable efficiency for external current drive through electron-cyclotron waves in a demonstration tokamak reactor is investigated. Two possible reactor designs, one for steady state and one for pulsed operation, are considered. Beam propagation, absorption and current drive are modelled employing the beam-tracing technique and including momentum conservation in electron–electron collisions. It is found that for midplane injection the achievable current drive efficiency is limited by second-harmonic absorption at levels consistent with previous studies. Higher efficiencies can be achieved by injecting the beams from the top of the machine, exploiting wave absorption by more energetic (less collisional) electrons. Current drive efficiencies competitive with those usually obtained by neutral beam current drive are reported. These optimum efficiencies are found for frequencies around 230 GHz and 290 GHz for the steady-state and the pulsed DEMO, supposed to operate at a magnetic field B = 5.84 T and B = 7.45 T, respectively.

/pdf/electron-cyclotron-current-drive-efficiency-in-demo-plasmas-4ce0uwuppf.pdf

Electron-cyclotron-current-drive efficiency in DEMO plasmas

/pdf/plasma-physics-and-controlled-fusion-conference-focussing-on-1xynw1lyj8.pdf

P.E. Stott

Papers

Plasma Physics and Controlled Fusion Conference: Focussing on Tokamak Research