Determination of the power absorbed during plasma ECR heating from diamagnetic measurements
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Determination of the Power Absorbed during Plasma ECR Heating from Diamagnetic Measurements L. M. Kovrizhnykh Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, 119991 Russia e-mail: [email protected] Received June 8, 2016; in final form, August 25, 2016
Abstract―Probable reasons are discussed why the absorbed energy determined from diamagnetic measurements in experiments on electron cyclotron resonance plasma heating is less than the input microwave energy. DOI: 10.1134/S1063780X17040067
1. INTRODUCTION When studying the plasma heating efficiency and energy lifetime in toroidal magnetic confinement systems, various scalings derived from numerous experimental data obtained at different devices are used. The scalings concerning high-frequency plasma heating usually operate with the input power, rather than with the power absorbed by plasma. Note that the absorbed power is rather difficult to determine experimentally. Currently, there are two methods to measure this power. The first, relatively simple method consists in measuring the response of the magnetic flux to the change in the plasma pressure. The second, more complicated method requires direct measurements of the plasma energy (i.e., the plasma density and temperature). In the experiments carried out at the L-2M stellarator with the use of the first method, rather surprising and strange results were obtained. According to diamagnetic measurements, the power absorbed by plasma during electron cyclotron resonance heating (ECRH) was appreciably less than the input power. Thus, it was unclear where the unabsorbed fraction of the input power was lost [1, 2]. On the other hand, measurements of the microwave damping length and single-path absorption [3] demonstrated almost complete microwave power absorption in the L-2 plasma, which agrees with ray-tracing calculations but contradicts the results of diamagnetic measurements. In this paper, we will discuss probable reasons for this contradiction. 2. MATHEMATICAL MODEL Let us use a simplified model based on the heat conduction equation
3 ∂ p = K 1 ∂ r ∂ p + S (t, r ), 2 ∂t r ∂r ∂r
(1)
where p = nTe(t) is the electron pressure, Тe is the electron temperature, K is the thermal diffusivity, and S (t, r ) is the input microwave power. We introduce the dimensionless variables x = r/r0, N = n/N0, T(t) = Te(t)/T0, and P = NT, where r0 is the minor plasma radius and N0 and T0 are some arbitrary constant values of the particle density and temperature. We assume that the plasma density is independent of time and the temperature is independent of the х coordinate. We also assume the thermal diffusivity to be
K = K 0T α , where the coefficient K0 is independent of the x coordinate and temperature Т. The input power S can be written as S(t) = nTin(t)T0/τ, where τ = r02 /K0 is the characteristic heat diffusion time and the dimensionless function Tin(t) describes the dependence of the input microwave power on time t (which will further be normalized to τ). Assuming that N(x) = N0(x) = J0(kx), wher
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