7.6 Fast electron magnetic ripple losses

This simulation is here again presented to illustrate code capabilities for a realistic magnetic configuration and a hot plasma. The problem addressed corresponds to fast electron losses in magnetic ripple, between two consecutive toroidal magnetic field coils. The case studied correponds only for the Tore Supra tokamak, which exhibits a very large magnetic ripple on the outer plasma edge, of the order of 7% [?]. Though the description of the physical process is not fully consistent with the basic assumptions of the code, and the bounce-averaged theory especially, calculations are expected to give valuable informations of the loss rate profile.

Simulations parameters are exactly those used in Sec.7.5 for fast electron transport studies, except that the magnetic configuration corresponds to the tokamak Tore Supra which has a circular plasma cross-section, and that fast electron radial transport is here neglected. Moreover, the magnetic ripple losses are modelized by a characteristic loss (drift) time ν_dST^-1 = 1000 inside the supertrapped domain bounded by ≤ ξ_0ST and p ≳ p_c as discussed in Sec.3.6.

Temperature and density profiles used as input for the magnetic equilibrium calculations done by HELENA code are presented in Fig. 7.38. As usual in current drive regime at low density, the electron temperature profile is peaked, and its value is much larger than ion temperature. The dominant ion (deuterium) profile is determined selfconsistently from the electron density and effective charge profiles, the latter being taken flat at a level of Z_eff = 1.5. In the calculations which are based on electroneutrality, only one fully stripped impurity is considered, i.e. carbon Z_s = 6, in order to avoid the use of an impurity transport code. The resulting 2 - D contour plot of the magnetic poloidal flux surfaces is given in Fig. 7.39, where the Shafranov shift is clearly visible. Here, calculations are performed for a monotonic safety factor profile, like for the JET case discussed in the previous section.

In order to be concerned by more energetic electrons in this simulation, the Lower Hybrid quasilinear resonance domain is slightly at higher energy, i.e. , with the same radial profile dependence of D_0,new^LH as discussed in Sec. 7.5. The RF power absorption takes place close to ρ ≃ 0.4 as shown in Fig.7.40. In this case, the current density and RF power absorption profiles are aligned, since the physics is basically local (slowing-down).

As shown in Fig. 7.41, the fact electron loss rate exhibits a clear peak at ρ ≃ 0.7, as observed experimentaly. The 3 - D calculations reproduce therefore correctly the profiles given by previous studies with a 2 - D Fokker-Planck code [?]. In addition, the two methods used to evaluate the magnetic ripple loss rate profile, as discussed in Sec.3.6 gives very similar quantitative results, that makes the code very reliable concerning this problem.

The detailed dynamics in momentum space is given by the 2 -D contour plot. As shown in Fig.7.42 at the radial position ρ ≃ 0.44, the supertrapped domain defined by ≤ ξ_0ST in which electrons are considered as lost lies well inside the domain where electrons are trapped ≤ ξ_0T . The collisional detrapping threshold is approximately p_c = 5 at the local density here presented. The effect of the magnetic ripple losses may be clearly seen on the distribution function f₀ which drops dramatically above p_c provided ≤ ξ_0ST . It is important to show that outside from this domain, the electron distribution function is nearly similar to the one without magnetic ripple losses. This is particularly clear in Fig.7.43. This confirms that losses are very small, and this is the reason why the code remains globally conservative at each radial location.