Abstract
The potential for damage, the magnitude of the extrapolation, and the importance of the atypical—incidents that occur once in a thousand shots—make theory and simulation essential for ensuring that relativistic runaway electrons will not prevent ITER from achieving its mission. Most of the theoretical literature on electron runaway assumes magnetic surfaces exist. ITER planning for the avoidance of halo and runaway currents is focused on massive-gas or shattered-pellet injection of impurities. In simulations of experiments, such injections lead to a rapid large-scale magnetic-surface breakup. Surface breakup, which is a magnetic reconnection, can occur on a quasi-ideal Alfvénic time scale when the resistance is sufficiently small. Nevertheless, the removal of the bulk of the poloidal flux, as in halo-current mitigation, is on a resistive time scale. The acceleration of electrons to relativistic energies requires the confinement of some tubes of magnetic flux within the plasma and a resistive time scale. The interpretation of experiments on existing tokamaks and their extrapolation to ITER should carefully distinguish confined versus unconfined magnetic field lines and quasi-ideal versus resistive evolution. The separation of quasi-ideal from resistive evolution is extremely challenging numerically, but is greatly simplified by constraints of Maxwell’s equations, and in particular those associated with magnetic helicity. The physics of electron runaway along confined magnetic field lines is clarified by relations among the poloidal flux change required for an e-fold in the number of electrons, the energy distribution of the relativistic electrons, and the number of relativistic electron strikes that can be expected in a single disruption event.
Highlights
The danger to the ITER mission posed by runaway electrons became apparent two decades ago [1,2,3]
The theory of runaway electrons on confined magnetic field lines [25] is circumscribed by: (1) the number of energetic electrons remaining after a thermal quench, (2) the kinetic energy Kr required by an electron to runaway, and (3) the change in the poloidal flux γef ψpa required for an e-fold in the number of energetic electrons
In devising a strategy to avoid this transfer and in using data from existing tokamaks to provide evidence for the effectiveness, two pairs of concepts are of central importance: 1. Destruction versus preservation of magnetic surfaces during thermal quenches. (a) Magneticsurfacesappeartobedestroyedwithin∼ 1ms, over much of the plasma volume during a thermal quench. (b) Electrons can be accelerated to relativistic energies only in flux tubes in which the magnetic field lines remain confined and some surfaces persist
Summary
The danger to the ITER mission posed by runaway electrons became apparent two decades ago [1,2,3]. Unless the plasma viscosity is sufficiently large, the inertial force is required, and j∥/B relaxes to an equilibrium value on the time scale for a shear Alfvén wave to propagate along the magnetic field lines and cover the region over which the reconnection occurred [10], ∂2( j∥/B)/∂t2 = V 2A∂2( j∥/B)/∂ 2. Magnetic surfaces can be broken on a quasi-ideal, Alfvénic rather than resistive, time scale, a parallel electric field, such as that due to the plasma resistivity η, is required to accelerate electrons along magnetic flux tubes that do not intercept the chamber walls, section 2.3.1. Studies of electron runaway in existing experiments require an understanding of (1) magnetic surface breakup and (2) the implications for electron acceleration due to the plasma resistivity within the remaining tubes of non-intercepting magnetic field lines. The required level of control is probably beyond what can be achieved
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