Analysis of the Synchrotron Radiation Emitted by Runaway Electrons

Analytical expressions are obtained that enable us to analyze the observed spot of synchrotron radi­ ation emitted by runaway electrons with the finite ratio V.liVjI' where V.l and Vjl are the transverse and longitu­ dinal (with respect to the confining magnetic field) velocities of the electrons. The safety factor q(r), the hori­ zontal displacement of the drift surfaces with respect to the magnetic ones, and the position of ,the detector are taken into account. Some uncertainties that may arise in this analysis are examined. Conditions that are typical of experiments carried out in the TEXTOR tokamak are considered. An experimental technique based on an analysis of the synchrotron radiation emitted by highly relativistic electrons is used in the TEXTOR tokamak to study the parameters of runaway electrons with the finite ratio V.l/v lI , where v.l and Vii are the transverse and longitu­ dinal (with respect to the confining magnetic field) velocities of the electrons (1-3). By measuring the sizes of the observed spot of the synchrotron radiation emitted by runaway electrons, it was possible to esti­ mate the ratio V.l/vu . It was found that V.l/Vil = 0.1. A spectral analysis of the radiation showed that the maximum energy of runaway electrons ranges from 25 to 30 MeV. The measurement of the absolute intensity of radiation made it possible to estimate the number of runaway electrons. Beams of runaway electrons with the large ratio v.l/ Vii are produced as a result of the secondary expUlsion of thermal electrons into the runaway region (P.l > P.lcr) by fast tail electrons 1 (4). Here, P.l is the transverse momentum,p.ler =Vfipcr/3, P~r =81t'leI 3 nLmeE- 1 (1 + 0.5z;), n is the density of thermal particles in the plasma, L is the Coulomb logarithm, e and me are the charge and mass of an electron, E is the accelerating electric field, and Zi is the ion charge number. Recall that Sokolov (5) was the first to estimate the effect of close collisions on the amount of runaway electrons in tokamaks. This effect is typical of present-day tokamak experiments with a large duration of discharges when the energy of the tail electrons amounts to tens of mega­ electron volts and more. In this case, there appear beams of electrons with transverse momenta lying in the range 112 that the confinement of ultrarelativistic electrons with larger values of P.l is better when the electron slowing down due to radiation is balanced by a force caused by the accelerating electric field, because, according to (6), for particJes with larger values of P.l, the slowing down due to radiation is more significant. In order to estimate the ratio v.l/ VII correctly, we must carefully analyze the experimental data. In the present paper, we derive equations describing the posi­ tions of electrons that emit synchrotron radiation recorded by a detector. We also show how these equations can be used to interpret the results of measurements.