$\beta$-Induced Alfvén Eigenmodes Destabilized by Energetic Electrons in a Tokamak Plasma

The $\beta$-induced Alfvén eigenmode (BAE) excited by energetic electrons has been identified for the first time both in the Ohmic and electron cyclotron resonance heating plasma in HL-2A. The features of the instability, including its frequency, mode number, and propagation direction, can be observed by magnetic pickup probes. The mode frequency is comparable to that of the continuum accumulation point of the lowest frequency gap induced by the shear Alfvén continuous spectrum due to finite $\beta$ effect, and it is proportional to Alfvén velocity at thermal ion $\beta$ held constant. The experimental results show that the BAE is related not only with the population of the energetic electrons, but also their energy and pitch angles. The results indicate that the barely circulating and deeply trapped electrons play an important role in the mode excitation.

Figure 1

HL-2A pulse no. 10 579. (a) Central line-average density, (b) magnetic probe signal, (c) the spectrogram of magnetic probe signal. Plasma current $I_p=160\mathrm{kA}$, toroidal field $B_t=1.3\mathrm{T}$, central ion and electron temperature $T_i\sim 0.85\mathrm{keV}$, $T_e\sim 1.10\mathrm{keV}$, edge safety factor $q_a\approx 4.0$, ECRH power $P_{\mathrm{ECRH}}=1.0\mathrm{MW}$, off-axis heating at LFS and NBI power $P_{\mathrm{NBI}}=0.38\mathrm{MW}$.

Figure 2

HL-2A pulse no. 13 364. (a)–(c) Counts of hard-x-ray (HXR) photons at different energy ranges, (d) central line-average density, (e) magnetic probe signal, (f) the spectrogram of magnetic probe signal. Plasma current $I_p=320\mathrm{kA}$, toroidal field $B_t=2.4\mathrm{T}$, central electron temperature, $T_e\sim 2.3\mathrm{keV}$, edge safety factor $q_a\approx 4.0$, and ECRH power $P_{\mathrm{ECRH}}=1.41\mathrm{MW}$, on-axis heating.

Figure 3

HL-2A pulse no. 10 580. (a) Central line-average density and nonthermal radiation measured by ECE, (b) magnetic probe signal, (c) the spectrogram of magnetic probe signal. Plasma current $I_p=160\mathrm{kA}$, toroidal field $B_t=1.3\mathrm{T}$, central ion and electron temperature $T_i\sim 0.50\mathrm{keV}$, $T_e\sim 0.62\mathrm{keV}$, edge safety factor $q_a\approx 4.0$, and ECRH power $P_{\mathrm{ECRH}}=0.89\mathrm{MW}$, off-axis heating at LFS.

Figure 4

The mode frequencies versus the Alfvén velocity. (a) ECRH plasma, (b) Ohmic plasma. Marker point (●) denotes raw data. Solid line denotes linear fit result.

Figure 5

The frequency of the BAE accumulation point versus ion temperature at $q=3$ surface. $\tau =T_e/T_i$.