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

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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.