## Periodic Reporting for period 3 - PLASMA (Running away and radiating)

Reporting period: 2018-10-01 to 2020-03-31

"Particle acceleration and radiation in plasmas has a wide variety of applications, ranging from cancer therapy and lightning initiation, to the improved design of fusion devices for large scale energy production. The goal of this project is to build a flexible ensemble of theoretical and numerical models that describes the acceleration processes and the resulting fast particle dynamics in two focus areas: magnetic fusion plasmas and laser-produced plasmas.

The fundamental questions that are addressed in this project are: (1) how are the particles raised from the thermal level to higher energies, (2) what are the dynamics of and the radiation emitted by these particles and (3) how do the superthermal particles affect the rest of the plasma. Radiation here is used in a broad sense: it includes electromagnetic waves and particle generation (e.g. neutron or positron production).

The project is focused on questions relevant to magnetic fusion plasmas and laser-produced plasmas. The solutions, however, are constructed in a general way, which allows extension to other types of plasma (e.g. magnetospheric plasmas, solar flares). The motivation to study charged particle beam formation is different in the two focus areas: in magnetic fusion plasmas an important concern is the generation of runaways and in laser-produced plasmas the interest concerns advanced radiation sources. It is from these that the title of the project, ""Running away and Radiating"", stems.

Predictions show that a major part of the initial plasma current in large fusion devices of the tokamak type, such as ITER, can be converted to runaway electron current in a disruption. The subsequent uncontrolled loss of a runaway beam could lead to melting of the plasma facing components. Thus, studies are urgently needed to find ways to mitigate the detrimental effects of runaway electron beams. As the plasma current in present devices cannot be increased above a few mega-amperes, experimental simulation of reactor-scale high-current tokamak disruptions is not possible. Experimental data must be used for validation of theoretical and numerical models, that will be exploited to predict runaway generation and suggest mitigation strategies in next-step fusion devices. This is at the focus of the PLASMA project and through this the project has great impact on the safety and reliability of next generation magnetic fusion devices.

The electron and ion beams produced in plasma-based accelerators have very attractive properties, e.g. ultra-short duration at the source, large particle number and high degree of laminarity (low transverse emittance). Plasma-based particle and radiation sources could therefore be suitable for a wide range of novel applications, such as ultrafast studies of condensed matter, radiotherapy, production of short lived isotopes for medical diagnostics, non-destructive inspection of materials, injectors for conventional accelerators, study of cosmic radiation damage to spacecraft components etc. Some applications employ the unique properties of laser-driven beams. In other applications, where short beam pulse duration is not essential, and conventional accelerators can be employed, plasma-based accelerators can still be advantageous if they provide similar beam characteristics with smaller installation size and operation cost. The PLASMA project provides new theoretical tools in the field of plasma-based acceleration, and suggests methods for optimizing plasma-based acceleration regarding stability and efficiency. This will bring plasma-based radiation sources closer to applications."

The fundamental questions that are addressed in this project are: (1) how are the particles raised from the thermal level to higher energies, (2) what are the dynamics of and the radiation emitted by these particles and (3) how do the superthermal particles affect the rest of the plasma. Radiation here is used in a broad sense: it includes electromagnetic waves and particle generation (e.g. neutron or positron production).

The project is focused on questions relevant to magnetic fusion plasmas and laser-produced plasmas. The solutions, however, are constructed in a general way, which allows extension to other types of plasma (e.g. magnetospheric plasmas, solar flares). The motivation to study charged particle beam formation is different in the two focus areas: in magnetic fusion plasmas an important concern is the generation of runaways and in laser-produced plasmas the interest concerns advanced radiation sources. It is from these that the title of the project, ""Running away and Radiating"", stems.

Predictions show that a major part of the initial plasma current in large fusion devices of the tokamak type, such as ITER, can be converted to runaway electron current in a disruption. The subsequent uncontrolled loss of a runaway beam could lead to melting of the plasma facing components. Thus, studies are urgently needed to find ways to mitigate the detrimental effects of runaway electron beams. As the plasma current in present devices cannot be increased above a few mega-amperes, experimental simulation of reactor-scale high-current tokamak disruptions is not possible. Experimental data must be used for validation of theoretical and numerical models, that will be exploited to predict runaway generation and suggest mitigation strategies in next-step fusion devices. This is at the focus of the PLASMA project and through this the project has great impact on the safety and reliability of next generation magnetic fusion devices.

The electron and ion beams produced in plasma-based accelerators have very attractive properties, e.g. ultra-short duration at the source, large particle number and high degree of laminarity (low transverse emittance). Plasma-based particle and radiation sources could therefore be suitable for a wide range of novel applications, such as ultrafast studies of condensed matter, radiotherapy, production of short lived isotopes for medical diagnostics, non-destructive inspection of materials, injectors for conventional accelerators, study of cosmic radiation damage to spacecraft components etc. Some applications employ the unique properties of laser-driven beams. In other applications, where short beam pulse duration is not essential, and conventional accelerators can be employed, plasma-based accelerators can still be advantageous if they provide similar beam characteristics with smaller installation size and operation cost. The PLASMA project provides new theoretical tools in the field of plasma-based acceleration, and suggests methods for optimizing plasma-based acceleration regarding stability and efficiency. This will bring plasma-based radiation sources closer to applications."

Building a generalized model for collisions is of paramount importance for the project and it required new theoretical and numerical developments. We have implemented a relativistic nonlinear Fokker-Planck collision operator in a new numerical tool (NORSE) and we presented the first fully conservative large-angle collision operator, derived from the relativistic Boltzmann operator.

Bremsstrahlung and synchrotron radiation emission is an important energy loss mechanism for energetic electrons in plasmas. We investigated the effect of spontaneous bremsstrahlung emission on the momentum-space structure of the electron distribution, fully accounting for the emission of finite-energy photons. We found that the electrons, accelerated by electric fields, can reach significantly higher energies than expected from simple energy-loss considerations. Furthermore we investigated the effect of synchrotron radiation reaction on runaway electron dynamics using relativistic finite-difference Fokker-Planck codes. Under the action of radiation reaction, we found that a non-monotonic feature (a “bump”) is formed in the tail of the electron distribution function.

One of the most common ways for studying runaway electrons in experiments is to take images and measure the spectrum of the synchrotron radiation emitted by them. We developed a synthetic synchrotron diagnostic tool, SOFT, to model the synchrotron cameras used in experiments, and to simulate the images resulting from runaway electron synchrotron emission. Using SOFT, the dependence of the synchrotron image on electron energy, pitch angle, radial distribution and camera location has been investigated, allowing general conclusions to be drawn about the synchrotron image due to a population of runaway electrons.

We analysed the dynamics of fast electrons in plasmas containing partially ionized impurity atoms. A generalized collision operator was derived from first principles using quantum-mechanical models. We implemented the generalized collision operator in a Fokker-Planck solver, and demonstrated that interaction with partially ionized atoms greatly affects fast-electron dynamics by enhancing the rates of angular deflection and energy loss. In particular, we investigated the decay of a runaway-electron current coupled to a self-consistent electric field. The effect of the interaction with partially ionized impurities has important implications for the efficacy of mitigation strategies for runaway electrons in tokamak devices.

We developed a relativistic Eulerian Vlasov-Maxwell solver (VERITAS) with block-structured adaptive mesh refinement in one spatial and one momentum dimension. Using VERITAS we studied ion acceleration due to the interaction between a short high-intensity laser pulse and a moderately over-dense plasma target. The impact of variations in the plasma density profile and laser pulse parameters were investigated, and the interplay between collisionless shock and target normal sheath acceleration (TNSA) mechanisms was analysed. The existence and properties of low Mach-number electrostatic collisionless shocks was also investigated with a semi-analytical solution for the shock structure. We showed that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations. We found that even a small amount of impurities can influence the shock properties significantly, including the reflected light ion fraction, which can change several orders of magnitude.

We studied kinetic effects responsible for the transition to relativistic self-induced transparency in the interaction of a circularly-polarized laser-pulse with an over-dense plasma and their relation to ion acceleration. We reported on a new regime in which a transition from relativistic transparency to hole-boring occurs dynamically during the course of the interaction. It is shown that, for a fixed laser intensity, this dynamic trans

Bremsstrahlung and synchrotron radiation emission is an important energy loss mechanism for energetic electrons in plasmas. We investigated the effect of spontaneous bremsstrahlung emission on the momentum-space structure of the electron distribution, fully accounting for the emission of finite-energy photons. We found that the electrons, accelerated by electric fields, can reach significantly higher energies than expected from simple energy-loss considerations. Furthermore we investigated the effect of synchrotron radiation reaction on runaway electron dynamics using relativistic finite-difference Fokker-Planck codes. Under the action of radiation reaction, we found that a non-monotonic feature (a “bump”) is formed in the tail of the electron distribution function.

One of the most common ways for studying runaway electrons in experiments is to take images and measure the spectrum of the synchrotron radiation emitted by them. We developed a synthetic synchrotron diagnostic tool, SOFT, to model the synchrotron cameras used in experiments, and to simulate the images resulting from runaway electron synchrotron emission. Using SOFT, the dependence of the synchrotron image on electron energy, pitch angle, radial distribution and camera location has been investigated, allowing general conclusions to be drawn about the synchrotron image due to a population of runaway electrons.

We analysed the dynamics of fast electrons in plasmas containing partially ionized impurity atoms. A generalized collision operator was derived from first principles using quantum-mechanical models. We implemented the generalized collision operator in a Fokker-Planck solver, and demonstrated that interaction with partially ionized atoms greatly affects fast-electron dynamics by enhancing the rates of angular deflection and energy loss. In particular, we investigated the decay of a runaway-electron current coupled to a self-consistent electric field. The effect of the interaction with partially ionized impurities has important implications for the efficacy of mitigation strategies for runaway electrons in tokamak devices.

We developed a relativistic Eulerian Vlasov-Maxwell solver (VERITAS) with block-structured adaptive mesh refinement in one spatial and one momentum dimension. Using VERITAS we studied ion acceleration due to the interaction between a short high-intensity laser pulse and a moderately over-dense plasma target. The impact of variations in the plasma density profile and laser pulse parameters were investigated, and the interplay between collisionless shock and target normal sheath acceleration (TNSA) mechanisms was analysed. The existence and properties of low Mach-number electrostatic collisionless shocks was also investigated with a semi-analytical solution for the shock structure. We showed that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations. We found that even a small amount of impurities can influence the shock properties significantly, including the reflected light ion fraction, which can change several orders of magnitude.

We studied kinetic effects responsible for the transition to relativistic self-induced transparency in the interaction of a circularly-polarized laser-pulse with an over-dense plasma and their relation to ion acceleration. We reported on a new regime in which a transition from relativistic transparency to hole-boring occurs dynamically during the course of the interaction. It is shown that, for a fixed laser intensity, this dynamic trans

Understanding runaway electron (RE) dynamics in suddenly cooling impure plasmas is vital for developing schemes aimed at mitigating the effects of RE in future fusion devices. It requires self-consistent coupling of the kinetic equation solvers to the electric field evolution which is governed by Maxwell’s equations, which is a considerable challenge. Our numerical tools provide the means to simulate RE dynamics self-consistently and allow for more complete and systematic comparisons with experimentally measurable quantities, which is a considerable improvement compared with the state of the art. During the first half of the project we have reached many of the important milestones in this direction; we have derived sophisticated models for collisions, nonlinear effects, more accurate treatment of dynamic scenarios, effect of radiation and partially screened impurities. We develop also synthetic diagnostic tools which are essential for experimental comparisons.

With regard of the laser-produced plasmas, the focus of the PLASMA project has been laser-solid interactions, in particular target-normal-sheath-acceleration, shock-waves and magnetic reconnection. These processes require fully kinetic modelling, and are addressed using semi-analytical models complemented by Eulerian and Particle-in-Cell simulations. We have discovered several novel aspects of ion acceleration; a dynamic transition region to self-induced-transparency, origin of plateaus in the energy spectra, effect of impurities on shock-wave dynamics and associated ion acceleration. We have also demonstrated that ultrafast relativistic MR in a magnetically dominated regime can be triggered by a laser interacting with a micro-scale plasma slab.

With regard of the laser-produced plasmas, the focus of the PLASMA project has been laser-solid interactions, in particular target-normal-sheath-acceleration, shock-waves and magnetic reconnection. These processes require fully kinetic modelling, and are addressed using semi-analytical models complemented by Eulerian and Particle-in-Cell simulations. We have discovered several novel aspects of ion acceleration; a dynamic transition region to self-induced-transparency, origin of plateaus in the energy spectra, effect of impurities on shock-wave dynamics and associated ion acceleration. We have also demonstrated that ultrafast relativistic MR in a magnetically dominated regime can be triggered by a laser interacting with a micro-scale plasma slab.