Presented by: Chen Wei1 (陈伟) EX/5-3 Observation of GAM Induced by Energetic Electrons and NL Interactions among GAM, BAEs and Tearing Modes on the HL-2A Tokamak Presented by: Chen Wei1 (陈伟) Collaborator： X. T. Ding1, L. M. Yu1, M. Isobe2, X. Q. Ji1, Y. P. Zhang1, Z. B. Shi1, G. L.Yuan1, J. Q. Dong1, Q. W. Yang1, Yi. Liu1, L. W. Yan1, Y. Zhou1, B. B. Feng1, W. Li1, X. M. Song1, S. Y. Chen3, X. R. Duan1 and HL-2A team X. T. Ding1, L. M. Yu1, M. Isobe2, X. Q. Ji1, Y. P. Zhang1, Z. B. Shi1, G. L.Yuan1, J. Q.3College of Physical Science and Technology, Sichuan Univ., Chengdu610065 1Southwestern Institute of Physics, P.O. Box 432 Chengdu 610041, China 2National Institute for Fusion Science, Toki 509-5292, Japan 3College of Physical Science and Technology, Sichuan Univ., Chengdu 610065 24th IAEA Fusion Energy Conference, 8-13 October 2012, San Diego, USA

Outline Introduction 2) Characterization of BAE/EGAM during Strong TMs 3) Relationship between EEs and Mode Excitation 4) NL interactions among BAEs, EGAM and TM 5) Excitation Mechanism of EGAM 6) Summary

Introduction of EGAM/BAE EGAM ： observed and studied using counter-passing beam ions on DIII-D and LHD. Nazikian, PRL2008; Fu, PRL2008; Ido, NF2010; Qiu, PPCF2010 ,PST2011 and PoP2012; BAEs ：also observed and investigated under different conditions in toroidal plasma, including that driven by fast ions （DIII-D, TFTR, TS, AUG）, energetic electrons (HL-2A), and large magnetic islands (FTU,TEXTOR, HL-2A, LHD, EAST). Heidbrink, PoP1999; Annibaldi, PPCF2007; Lauber, PPCF2009, Nguyen, PPCF2009; Chen, NF2011 and PFR2012 Energetic electrons, HL-2A Magnetic islands, HL-2A Chen , NF2011 Chen , PRL2010 EGAM/BAEs ： affect plasma performance, and induce fast particle losses. EGAM/BAEs: be used as energy channels to transfer the fusion-born-alpha-particle energy to the thermonuclear plasma.

Characterization of BAE/EGAM during Strong TMs The line averaged density was detected by HCN. The mode-numbers are measured using a set of Mirnov probes. A new mode has been observed in the HL-2A low density Ohmic plasma, recently. This phenomenon is perfectly reproducible, and a typical discharge parameters are shown in left fig. A coherent MHD fluctuation is visible around 17.5 kHz from 1250 ms to 2500 ms. The experiments discussed here were performed in deuterium plasmas with plasma current Ip =150-170kA, toroidal field Bt =1.20-1.38T, and safety factor qa=4.2-4.6 at the plasma edge.

Characterization of BAE/EGAM during Strong TMs Poloidal mode number Toroidal mode number Cross-power spectra P12, correlation coefficient ρ12 of poloidal Mirnov signals and poloidal mode number m = 2. Cross-power spectra P12, correlation coefficient ρ12 of toroidal Mirnov signals and toroidal mode number n = 0.

Characterization of BAE/EGAM during Strong TMs Magnetic fluctuation intensity depends on the poloidal angles Zhou, PoP07

Characterization of BAE/EGAM during Strong TMs Density limit of EGAM mode An important feature of EGAM mode on HL-2A is that the mode is observed by the magnetic probes only when ne <0.5*1019m-3 without auxiliary heating in the case of Ip~155kA and Bt~1.21T. This result was obtained in special experiments with density scans 0.1*1019m-3<ne <1.5*1019m-3. Figure suggest show the density limit of BAEs and EGAM modes. The density of #20378 is lower than that of #20386, and the energetic-electron population is higher. The BAEs and EGAM are driven in the process of enhancements of EE population in the low density discharge (#20378), but the modes are not excited in the high density(#20386). Some experimental results on HL-2A suggest that the density limit is improved with ECRH+NBI heating (see poster ).

Relationship between EEs and Mode Excitation Experimental layouts of CdTe and NaI detectors on HL-2A. (a) top view; (b) cross-section view. Chordal distances of ch1-ch4 are rd=5, 9, 15 and 30 cm, respectively. The hard x-ray spectrum is obtained using pulse height analysis (PHA). The range of the hard X-ray spectrum is E = 10-200keV divided into many energy bins by the PHA-software setting. The temporal resolution of the system is 1ms, and the highest energy resolution is dE = 1keV . Enhancement of EEs during magnetic reconnection at different CdTe channels. Magnetic probe signal (a) and corresponding spectrogram (j). Hard X-ray counts in arbitrary unit, (b)-(i) and (k)-(r). Left column, rd = 30cm; Right column, rd = 5cm. (b) and (k), E = 10-20keV ; (c) and (l), E = 20-30keV ; (d) and (m), E = 30-40keV ; (e) and (n), E = 40-60keV ; (f) and (o), E = 60-80keV ; (g) and (p), E = 80-100keV ; (h) and (q), E = 100-140keV ; (i) and (r), E = 140-200keV .

Relationship between EEs and Mode Excitation Magnetic probe signal (a) and corresponding spectrogram (e). Hard X-ray counts in arbitrary unit, (b)-(d) and (f)-(h). Left column, rd = 5cm; Right column, rd = 30cm. (b) and (f), E =30-40keV ; (c) and (g); E = 40-60keV ; (d) and (h), E = 60-80keV. Energy distributions of EEs without and with BAEs and EGAM at different CdTe channels. Black, blue and red lines are corresponding to t=1100-1110ms, 1300-1310ms and 1480-1490ms, respectively. The abundant HXR data were achieved by four CdTe detectors on HL-2A, and experimental results indicated the BAEs during strong TMs were also driven by EEs in nature. During strong TM, the energy distributions of energetic-electrons are all enhanced at different CdTe channels, shown in Figure, and the non-Maxwell distribution beams exist in the core plasma, as a result, these EEs induce the excitation of BAEs and EGAM. (More details, please see poster EX/5-3).

Relationship between EEs and Mode Excitation Here, we need point out that the energetic electrons, which are generated by the Ohmic electric field and parallel electric field during magnetic reconnection, are passing particles rather than trapped ones. However, in such case the trapped electrons still exist in abundance, and they are produced by the anomalous Doppler instability (ADI). ADIs and sawteeth on ECE and soft X-ray signals corresponding to red rectangle region in left figure. Evolution of plasma parameters with ADI, BAEs and EGAM on HL-2A for shot #17459. The ADI causes the pitch angle scattering of energetic electrons. The ADI transfers energy from parallel to perpendicular motion. It is found that the non-thermal emissions measured by ECE are very high during strong TM, and the ECE signal has many upward jumps which are different from the regular sawteeth measured by the soft X-ray. These jumps make clear that the ADI is driven, i.e., some circulating electrons become trapped electrons.

Relationship between EEs and Mode Excitation Production process of BAE modes during strong TMs Plasma equilibrium without magnetic island Magnetic island Energetic electrons, Co and counter passing New SAW continuum, New GAP and BAE Magnetic reconnection + BAE excitation，propagating in two opposite directions Magnetic island rotation Two branch BAEs propagating in two opposite directions and fBAE2-fBAE1=2ftm Biancalani, PRL10 and PPCF11 The BAEs during strong TMs are excited by EEs in nature.

NL interaction between BAEs and GAM/ZFs HL-2A The squared bicoherence and summed squared bicoherence of a poloidal Mirnov signal. It is found that the nonlinear interaction between the fundamental nBAE = 1 (or nBAE = -1 ) BAE with fBAE and n = 1 TM with fTM at each different moment. The following matching conditions are satisfied among these modes, i.e. nTM+nBAE = n’BAE/GAM and fTM+fBAE = f’BAE/GAM for TM and BAEs. Moreover, the n = ±1 BAEs interact with TM further and create a multitude of BAEs/GAMs, and f’BAE/GAM = (k-1)*fTM+fBAE, n’BAE/GAM = (k-1)*nTM+nBAE, where k is positive integer. If only considering the fundamental frequencies of TM, BAEs and GAM, their nonlinear interaction relations are fBAE2-fBAE1 = 2fTM, fBAE2+fBAE1 = 2fGAM, and other expressions are fBAE = fGAM ±fTM (i.e., GAM+TM=>BAE) or fGAM = fBAE ±fTM (i.e., BAE+TM=>GAM). Need to point out here that the direction of wave energy transfer is unknown, and it needs to be assessed.

NL interaction between BAEs and GAM/ZFs Schematic diagram of multiscale interactions Magnetic island BAE Turbulence GAM EPs Destabilize Damping Excite Regulate Coupling/ Ex. energy Suppress/ Drive Cross-scale NL interaction e.g. MITG, etc. Cross-scale NL interaction, e.g. AITG, etc. Destabilize/damping Schematic diagram of interactions among magnetic island, BAE, GAM, turbulence and energetic-particles (EPs). AITG: Alfven modes driven by ion temperature gradient (ITG) [Zonca, PoP99]; MITG: magnetic island induced ITG modes[Wang, PoP09]. The phenomenon is a typical example with respect to multi-scale interactions. It refers to many physics aspects, such as magnetic island, ZF, SAW as well as turbulence, and need be understood synthetically and reproduced on simulation.

Excitation Mechanism of EGAM As we known, the energy transfer from energetic particle to the wave can be expressed by . Here, and are, respectively, the particle energy derivative of the distribution function of energetic particle and the derivative for the toroidal momentum. Free Energy Channel I: For the GAM, the driving free energy may directly come from the positive gradient of the distribution function and indirectly (because of n=0) from the radial derivative of distribution function by nonlinear interactions. Need to point out that the GAM is not driven by precessional resonance due to n=0 and is not excited by well circulating and deeply trapped electrons because their bounce/transit frequencies is too high to resonance with GAM mode, i.e., the wave-particle resonance conditions( ) do not satisfy. But the barely circulating/trapped electrons in the vicinity of the passing-trapped boundary may have little contributions for mode excitation owing to their low bounce/transit frequencies. Free Energy Channel II: The energetic-electrons induce BAEs, then the GAM is excited via the nonlinear interactions (i.e. three wave resonance) among BAEs and strong TM which is a pump wave. ==> +

Summary The experimental results on HL-2A indicated that the BAEs during strong TMs are excited by EEs in nature. The EGAM induced by EEs has been observed in HL-2A Ohmic plasma. The EGAM localizes in the core plasma, i.e. in the vicinity of q=2 surface, and is very different from one excited by the drift-wave turbulence in the edge plasma. The analysis indicated that the EGAM is provided with the magnetic components, whose intensities depend on the poloidal angles, and its mode numbers are m/n=2/0. There exist intense nonlinear interactions among EGAM, BAEs and strong TMs. The EGAM is most probably excited by EEs via three wave resonance and processional resonance. But the barely circulating/trapped electrons in the vicinity of the passing-trapped boundary may have little contributions for mode excitation, and more theoretical works are needed.

Thank you for your attention! Your advice and criticism are welcome. If you are interested in these results, please contact with me. Email: chenw@swip.ac.cn