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New Insight into Runaway Electrons Production and Confinement

G. Martin, M. Chatelier and C. Doloc Association Euratom-CE A, CEN Cadarache, 13108 Saint-Paul-lez-Durance, FRANCE

1. Introduction

Runaway Electron avoidance and control are both important issues for future large Tokamaks like ITER. Runaway Electrons have been observed on toroidal devices since their very beginning, that is for more than 40 years. On small machines they were produced primarily during the "break-down" or "current plateau" phase of plasma pulses and could be avoided after some operation time or by working at sufficiently high density or in clean machines. On present large devices like JET, JT60U, TFTR or Tore Supra, they are produced in large amounts during disruptions, with the noticeable exception of DIII-D where none have been detected [1]. They might prove detrimental for first wall components, especially in actively cooled devices. Reliable models, for both creation, energy limit, confinement and loss are still needed to explain or predict the behaviour of these electrons. Important features that a model should accommodate are discussed on the grounds of several years of observations on Tore-Supra and other devices. A code has been developed to show easily where damages are to be expected.

2. Classical Runaway Electron Creation Rates

The runaway electron creation process during the current plateau of tokamak discharges has been well understood on small tokamaks [3]. The plateau production depends strongly on plasma density and much more weakly on other parameters like e.g. the toroidal field. Extrapolations to future devices can be made with some confidence, although they are not very useful since this source of electrons is generally weak enough to be ignored. The large amounts of runaway electrons produced during plasma current disruptions on present days large tokamaks seem to follow quite different rules as observed on Tore Supra. • On figure 1, the number of photo-neutrons detected during disruptions for a variety of pre- disruptive condition: is plotted (this number can give a good estimate ef the number of electrons accelerated to energies well above 10 MeV). While photo-neutron production does not seem to depend on the pre-disruptive plasma density over a broad range (1-5 1019nr3), it increases significantly with the value of the toroidal magnetic field. Below 2T, photo-neutrons are only rarely detected (coherently with DIHD results which always works below 2T?). At 3.8T, the value for present experiments, systematic photo-neutron production is observed. -98-

1E+08 0,50 1.00 1,50 2,00 Pre-Dferuptive Plasma Current

|1

E+15 •

E+14O

E+13 • • • E+12 • o

E+11

E+10 • 4 E+09 1E+08 —i— E+08 1.50 2.00 2.50 3,00 3.50 4.00 1,00 2.00 3,00 4.00 5,00 Toroidal Field (Tesks) Mean Electron Density (10*19 m-3) Fig. 1: Photo-neutron production due to disruption induced runaway electrons on TORESUPRA (The 1(P line shows the detection limit: points below this limit are for neutron free disruptions)

3. Model for runaway electron creation

In classical models, plasma parameters evolve slowly compared to collision time scales, typical for electrons to cross the Dreicer limit. In disruptions this is no longer true: the thermal quench duration TqE is much shorter than thcmean collision time T^ for fast electrons. One of-, the most strildng feature of disruptions is the fact that this duration is more or less the same on all tokamaks, irrespective of their size. On figure 2, tmn (a vVnJ has been plotted for supra- thermal electrons in a typical plasma at 4.1019nr3. It can be seen that 6-10 keV electrons loose only a small fraction of their energy by collision during the typical 0.5 ms duration of the thermal quench. -99-

During the thermal quench, the stored energy is lost through two channels: radiation, enhanced by impurity influx and lower temperature, and transport due to a partial ergodisation of the magnetic structure. This suggests a natural model in which the fate of the electrons depends on their initial energy: % The colder bulk experiences a high collision rate and strong interaction with impurities. Electrons lose their energy mainly through radiation on a time scale dominated by atomic physics: the observed "collapse duration", which does not change from one tokamak to the other, being due to local phenomena. •^ The hotter tail is more sensitive to field ergodisation. These electrons are less collisional and travel more rapidly along the field lines. They are lost in a diffusive process, which means that their number decreases exponentially with time. At the end of the quench, when the magnetic track restores, some of these fast electrons are still there. Due to the low temperature of the bulk, the Dreicer limit is then very low, and all these residual electrons "run away".

ne = 4.10*19 m-3/Te = 1 keV 2.0,

1.6; \F(Te) / 0,8 O.4| ^^^^^^^^^ Electron Energy (keV) 2.0 4.0 6,0 8,0

Fig 2: Typical Collision Time for fast Electrons (ms)

In this model, the density does not play a dominant role, but the magnetic field and the size of the device do. It has been observed that runaway electrons confinement is better for stronger field during plateau conditions [3]. The diffusion process of fast electrons is greatly enhanced in low field plasma (D a v.(5B/B)2), and the number of electron still there at the end of the quench depends exponentially on the field strength, as well as on the small radius of the plasma.

This model is still qualitative: we lack the precise measurements needed 'during the quench phase to put real numbers on the phenomena. It is anyhow possible to check that the order of magnitude and tendencies are correct. In particular, the number of runaways is always a small fraction of the number of the electrons initially carrying the plasma current, and this fraction varies from one disruption to the other, as expected from a diffusive loss mechanisms. -100-

Runaway Electron Trajectography

To follow electron trajectories after their creation, with the main goal of determining possible impact location, a new method has been developed. Initially conceived for fusion products [4], the code uses adiabatic theory. Collisionless fast particles are followed in the magnetic topology aid of the conservation of three invariant: ^ Their energy, which change very slowly on the cyclotron characteristic time. ^> The magnetic momentum, which is supposed to be equal to zero for runaways. ^ The toroidal momentum: L E 2n.m.vn.R+q.AP(R,Z).R The magnetic potential A^ is related to the vertical flux function *F The poloidal projection of the trajectory can then be represented by equation {I}: pp(R,Z) = -^-.—+

Larmor radius of the electron ^"''f'^foo = 0.0160.0166—6 ^—La and cp0 is defined by the initial e.ftQ.IIP I{IP{MA)) position of the electron. The structure of equation {1} suggests a graphical method to find easily the trajectory : it will be represented by the intersection of the flux function, a usually available equilibrium parameter, and an oblique plane. The slope of this plane is determined by the electron energy and plasma current ratio. An example is given on figure 3.

Flux

2=0

FLUX MAP TRAJECTORIES

Fig 3: Graphical determination of Runaway Trajectories. [\] Proceedings from the IAEA TCM on Tokamak Disruption, Culham Laboratory, 10-12 Sep. 1991. [2] J.W. Connor and RJ.Hastie, Nuclear Fusion 15 p415,1975 [3] M. Altman et al., Nuc. Inst. and Meth. 215 p453,1983 [4] C. Doloc et al, accepted to be published in Physic of Plasma, Princeton, 1995