Momentum-space dynamics of runaway electrons in plasmas
Doktorsavhandling, 2017

Fast electrons in a plasma experience a friction force that decreases with increasing particle speed, and may therefore be continuously accelerated by sufficiently strong electric fields. These so-called runaway electrons may quickly reach relativistic speeds. This is problematic in tokamaks – devices aimed at producing sustainable energy through the use of thermonuclear fusion reactions – where runaway-electron beams carrying strong currents may form. If the runaway electrons deposit their kinetic energy in the plasma-facing components, these may be seriously damaged, leading to long and costly device shutdowns. Crucial to the runaway phenomenon is the behavior of the runaway electrons in two-dimensional momentum space. The interplay between electric-field acceleration, collisional momentum-space transport, and radiation reaction determines the dynamics and the growth or decay of the runaway-electron population. In this thesis, several aspects of this interplay are investigated, including avalanche multiplication rates, synchrotron radiation reaction, modifications to the critical electric field for runaway generation, rapidly changing plasma parameters, and electron slide-away. Two numerical tools for studying electron momentum-space dynamics, based on an efficient solution of the kinetic equation, are presented and used throughout the thesis. The spectrum of the synchrotron radiation emitted by the runaway electrons – a useful diagnostic for their properties – is also studied. It is found that taking the electron distribution into account properly is crucial for the interpretation of synchrotron spectra; that a commonly used numerical avalanche operator may either overestimate or underestimate the runaway-electron growth rate, depending on the scenario; that radiation reaction modifies the critical electric field, but that this modification often is small compared to other effects; that electron slide-away can occur at significantly weaker electric fields than expected; and that collisional nonlinearities may be significant for the evolution of runaway-electron populations in disruption scenarios.

synchrotron radiation


critical electric field

non-linear collision operator


runaway electrons

fusion-plasma physics

PJ-salen, Origohuset, Fysikgården 2
Opponent: Dr. Abhay Ram, Plasma Science and Fusion Center, Massachusetts Institute of Technology, USA


Adam Stahl

Chalmers, Fysik, Subatomär fysik och plasmafysik

Kinetic modelling of runaway electrons in dynamic scenarios

Nuclear Fusion,; Vol. 56(2016)p. 112009-

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Synchrotron radiation from a runaway electron distribution in tokamaks

Physics of Plasmas,; Vol. 20(2013)p. 093302-

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NORSE: A solver for the relativistic non-linear Fokker-Planck equation for electrons in a homogeneous plasma

Computer Physics Communications,; Vol. 212(2017)p. 269-279

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Effective Critical Electric Field for Runaway-Electron Generation

Physical Review Letters,; Vol. 114(2015)p. 115002-

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Runaway-electron formation and electron slide-away in an ITER post-disruption scenario

Journal of Physics: Conference Series,; Vol. 775(2016)p. 012013-

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Numerical calculation of the runaway electron distribution function and associated synchrotron emission

Computer Physics Communications,; Vol. 185(2014)p. 847-855

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The life of a fast electron is never dull. In a plasma – a gaseous mix of constantly interacting charged particles – there are many forces and mechanisms at play. Some of them are unique to fast particles, for instance the emission of synchrotron radiation. Others, such as collisions with the other particles in the plasma, are common occurrences that have special implications for the fast particles. One curious consequence of the combination of these mechanisms is that fast particles (electrons in particular) can experience the so-called runaway phenomenon and be accelerated to extremely high speeds (very close to the speed of light, which is the absolute cosmic speed limit). This thesis is concerned with describing and simulating the behavior of such runaway electrons and the radiation they emit. Although the runaway phenomenon is interesting in itself, it also has potentially far-reaching consequences. Runaway electrons are a serious problem in fusion reactors – devices that seek to provide clean, safe, and reliable large-scale power production by harnessing the energy released when heavy hydrogen nuclei fuse together. In a fusion reactor, the hydrogen fuel exists in the form of a plasma, and under certain circumstances the electrons in that plasma may experience runaway acceleration. When those runaway electrons strike the walls of the device, they can cause great damage which must be avoided. For fusion to become a reliable energy source, the formation and suppression of runaway electrons must be understood and explored, and the work presented in this thesis is part of that effort. As new larger fusion devices (and eventually full-scale power plants) start operation in the coming decades, the issue of runaway electrons will only become more important since their generation increases strongly with machine size. Since fusion power has the potential to become the cornerstone of a sustainable energy system, better understanding of the runaway-electron phenomenon is therefore of great importance in the fight against the warming of the global climate.


Hållbar utveckling




Grundläggande vetenskaper


Fusion, plasma och rymdfysik



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4213


Chalmers tekniska högskola

PJ-salen, Origohuset, Fysikgården 2

Opponent: Dr. Abhay Ram, Plasma Science and Fusion Center, Massachusetts Institute of Technology, USA