Conquest of relativistic effect in the electron temperature measurement from electron cyclotron emission

通过对托卡马克低场侧二次谐波电子回旋辐射（ECE）的观测，测量了电子温度分布（T_e(r)）。二次谐波ECE测量的一个优点是可以很容易地得到T_e(r)的时间演化。当T_e较大时，相对论效应影响ECE测量的优劣。1)当T_e ~ 10keV时，由于二次谐波ECE的相对论性作用，T_e(r)发生了明显的位移。这种位移可以利用电子密度（n_e）的信息进行校正。然而，电子密度测量的误差取决于电子密度诊断的误差。2)当T_e大于20keV时，三次谐波ECE的相对论效应对二次谐波ECE产生影响，不能得到T_e(0)。研究的目的是利用数值计算构建对策。对于课题1)，我们证明了用ECE计算电子密度的可行性。也就是说，相对论性效应导致频率从非相对论性的EC频率移开。在托卡马克中，从高场侧可以有效地观测到相对论效应引起的频移。由于位移不仅取决于T_e和磁场，还取决于n_e，因此可以通过从低场侧和高场侧观测来测量n_e。对于题目2)，在球对称相对论性麦克斯韦分布函数的情况下，得到了斜向传播到磁场的发射率。我们证明了视线向赤道平面倾斜扩大了Te的可测区域。并对大型螺旋装置的相对论效应进行了评价。为了避免二次谐波的相对论性影响，天线的位置相对于等离子体轴应位于最大磁场的对面。

A electron temperature profile (T_e(r)) has been measured by observing second harmonic electron cyclotron emission (ECE) from low field side of tokamak. A merit of ECE measurement is that, the time evolution of T_e(r) is obtained from second harmonic ECE easily. When T_e is higher, relativistic effects affect the merit of ECE measurement. 1)In the case of T_e 〜10keV, T_e(r) obtained shifts apparently due to the relativistic effect of the second harmonic ECE. The shift can be corrected using information of the electron density (n_e). However, the error of ECE measurement depends on the error of electron density diagnostics. 2)When T_e is higher than 20keV, the relativistic effect of the third harmonic ECE affects on the second harmonic ECE, and T_e(0) can not be obtained. A purpose of the study is the construction of countermeasure using a numerical calculation. As for subject 1), we show that feasibility of electron density using ECE. That is, the relativistic effect results in the frequency shift from non-relativistic EC frequency. In a tokamak, the frequency shift due to the relativistic effect is observed from the high field side effectively. Since the shift depends on n_e as well as T_e and magnetic field, there is a possibility of the n_e measurement by observing from both low and high field sides. As for subject 2), the emissivity is obtained for the oblique propagation to the magnetic field in the case of the spherically symmetric relativistic Maxwellian distribution function. We show that the inclining the sight line to the equatorial plane expands the measurable region of Te. Moreover the relativistic effect is evaluated in Large Helical Device. In order to avoid the relativistic effect of 2nd harmonics, the antenna position should be at the opposite side of maximum magnetic field with respect to the plasma axis.