What is the fate of runaway positrons in tokamaks?

Abstract

Massive runaway positrons are generated by runaway electrons in tokamaks. The fate of these positrons encodes valuable information about the runaway dynamics. The phase space dynamics of a runaway position is investigated using a Lagrangian that incorporates the tokamak geometry, loop voltage, radiation and collisional effects. It is found numerically that runaway positrons will drift out of the plasma to annihilate on the first wall, with an in-plasma annihilation possibility less than 0.1%. The dynamics of runaway positrons provides signatures that can be observed as diagnostic tools.

Multi-scale full-orbit analysis on phase-space behavior of runaway electrons in tokamak fields with synchrotron radiation

“…For extremely energetic runaway electrons, their synchrotron radiation loss could be strong enough to balance out the acceleration by the loop electric field. The radiation dissipation then provides runaway electrons an upper bound of energy, i.e., the synchrotron energy limit [22][23][24][25]. The typical duration for a runaway electron with low energy (1keV-1MeV) to reach the energy limit has the order of magnitude of one second while the smallest timescale of Lorentz force is 10 −11 s [24,26], which means the dynamical behavior of runaway electrons spans about 11 orders of magnitude in timescale.…”

“…Fruitful results of this theory have been accomplished. Considering the gyro-center approximation regardless of the toroidal geometry, one can transfer the full-orbit dynamical equations of runaway electrons to a set of relaxation equations which are much easier to solve theoretically and numerically [24]. By use of relaxation equations, the momentum evolution structure as well as energy limit has been studied in detail under several kinds of dissipations, such as collision, synchrotron radiation, and bremsstrahlung radiation [22,23,27].…”

“…Both of these phenomena reflect the conservation of the toroidal canonical angular momentum. Recently, gyro-center simulations have been equipped with structure-preserving discrete methods and shown better long-term numerical accuracy than traditional methods [24,25,31].…”

Guiding-centre transformation of the radiation–reaction force in a non-uniform magnetic field

“…[11,12] is given only for a simple toroidal geometry and if one calculates the corresponding equations of motion using the Euler-Lagrange equation, the result does not give the "effective electric field" that they start with.…”

“…In Refs. [11,12], a rather different approach is adopted by treating the RRforce as an "effective electric field" which is then added into guiding-center Lagrangian as a time depending perturbation in the vector potential. This is not correct: the RR-force is of dissipative nature and no practical Lagrangian formulation exists within the framework of classical electrodynamics (here we do not discuss the quantum mechanical treatments).…”