Bulletin of the American Physical Society
APS April Meeting 2012
Volume 57, Number 3
Saturday–Tuesday, March 31–April 3 2012; Atlanta, Georgia
Session Q16: Sherwood III |
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Sponsoring Units: DPP Chair: Guoyong Fu, Princeton Plasma Physics Laboratory Room: Hanover FG |
Monday, April 2, 2012 10:45AM - 11:15AM |
Q16.00001: Nonlinear Frequency Chirping of $\beta $-induced Alfven Eigenmode Huasen Zhang The $\beta $-induced Alfven eigenmode (BAE) have been observed in many tokamaks. The BAE oscillates with the GAM frequency $\omega _0 $, and therefore, has strong interactions with both thermal and energetic particles. In this work, linear gyrokinetic particle simulations show that nonperturbative contributions by energetic particles and kinetic effects of thermal particles modify BAE mode structure and frequency relative to the MHD theory. Gyrokinetic simulations have been verified by theory-simulation comparison and by benchmark with MHD-gyrokinetic hybrid simulation. Nonlinear simulations show that the unstable BAE saturates due to nonlinear wave-particle interactions with thermal and energetic particles. Wavelet analysis shows that the mode frequency chirping occurs in the absence of sources and sinks, thus it complements the standard ``bump-on-tail'' paradigm for the frequency chirping of Alfven eigenmodes. Analysis of nonlinear wave-particle interactions shows that the frequency chirping is induced by the nonlinear evolution of coherent structures in the energetic particle phase space of ($\zeta $,$\omega _{\mbox{d}})$ with toroidal angle $\zeta$ and precessional frequency $\omega _{\mbox{d}}$. The dynamics of the coherent structures is controlled by the formation and destruction of phase space islands of energetic particles in the canonical variables of ($\zeta $,$\mbox{P}_\zeta)$ with canonical angular momentum $\mbox{P}_\zeta$. Our studies use the gyrokinetic toroidal code (GTC) recently upgraded with a comprehensive formulation for simulating kinetic-MHD processes. In collaborations with GTC team and SciDAC GSEP Center. [Preview Abstract] |
Monday, April 2, 2012 11:15AM - 11:45AM |
Q16.00002: Axiomatic approach to wave-particle interactions and its applications to waves with trapped particles I.Y. Dodin A general axiomatic approach is developed that yields ponderomotive Lagrangians for wave-particle collisionless interactions deductively and, often, without even referring to the Maxwell-Vlasov system [PRL {\bf 107} (2011) 035005; Phys. Plasmas {\bf 12} (2012) 012102, 102103, 102104]. From those, nonlinear dispersion relations and dynamic equations are derived, and, as a spin-off, the long-standing controversies are resolved pertaining to photon properties in dielectric medium. Langmuir waves with trapped electrons are studied as a paradigmatic example. For the case of deeply trapped electrons in particular, action conservation predicts different regimes depending on the energy flux $S$ carried by trapped particles. For example, the trapped-particle modulational instability (TPMI) can develop just due to large $S$, in contrast with the existing theories. Remarkably, this effect is not captured by the nonlinear Schr\"odinger equation, which is traditionally considered as a universal model of wave self-action. [Preview Abstract] |
Monday, April 2, 2012 11:45AM - 12:15PM |
Q16.00003: A five-field model of Peeling-Ballooning modes with BOUT++ T. Xia, X.Q. Xu, J. Li We extend the previous two-fluid 3-field ELM simulation model\footnote{X.Q.Xu, et. al., PRL, VOL. 105, 175005 (2010).} by separating the total pressure into density n$_{0}$, ion and electron temperature (T$_{e0}$, T$_{i0})$ equations. With diamagnetic drift, the growth rate is inversely proportional to n$_{0}$ because the diamagnetic drift is inversely proportional to n$_{0}$. The diamagnetic drift plays as the role of a threshold of the perturbation growth. Only the perturbations with the growth rate higher than this threshold can survive and begin to grow. Therefore, as density increases, the diamagnetic drift decreases and the stabilizing effect reduces as well. The diamagnetic drift is also proportional to toroidal mode number n, so at high n case, the peeling-ballooning mode is stabled by diamagnetic drift. For the same pressure profile, constant T$_{0}$ case increases the growth rate by 6.2{\%} compared with constant n$_{0}$ case in ideal MHD model. With diamagnetic effects, the growth is increased by 31.43{\%} for toroidal mode number n=15. This is because that the gradient of n$_{0}$ introduces the cross term in the definition of vorticity. This cross term has the destabilizing effect on peeling-ballooning mode. For the nonlinear simulation, the gradient of n$_{0}$ in the pedestal region can increase the energy loss of ELMs and drive the perturbation to go into the core region. The effects of parallel thermal conductivity will stabilize the growth of the turbulence and decrease the energy loss in the pedestal region. [Preview Abstract] |
Monday, April 2, 2012 12:15PM - 12:45PM |
Q16.00004: Nonlinearly unstable interchange modes in transverse magnetic field Jupiter Bagaipo, Adil Hassam, Parvez Guzdar The nonlinear stability of the ideal magnetohydrodynamic interchange mode for plasma immersed in a constant transverse magnetic field near marginal conditions is studied. We use reduced equations for a strong axial field to find an analytic solution for the nonlinear behaviour as a function of the deviation from marginality. The study is motivated in order to assess B-field tolerances in stellarator coil design. A systematic perturbation analysis in the smallness parameter, $|b_2/B_c|^{1/2}$, is carried out, where $B_c$ is the critical transverse magnetic field for the marginally stable ideal mode, and $b_2$ is the deviation from $B_c$. The lowest order expansion yields an eigenvalue equation for the magnitude of the critical field required for marginal stability, $B_c$. The calculation is carried out to third order, including nonlinear terms, and a time-evolution equation for the amplitude is found. In the short wavelength limit we find that the system is nonlinearly unstable for large enough perturbations even if $b_2/B_c>0$ (linearly stable). This result is similar to that of Cowley and Artun\footnote{S. C. Cowley and M. Artun, Physics Reports {\bf 283}, 185 (1997).} for the marginally stable line-tied $g$-mode. If the system is driven nonlinearly unstable, the resulting growt [Preview Abstract] |
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