"Progress in Understanding Fast-ion Transport by Instabilities: The Importance of Phase"

 

ABSTRACT:

 

For electrostatic modes, orbit-averaging effectively reduces the average potential experienced by the fast ion, resulting in smaller transport [1]. By definition, a resonant ion stays in phase with the wave for many wave periods. This results in energy transfer between the particle and the wave and, invariably, alters the constants of motion of the fast-ion orbit, causing transport. For small amplitude waves, resonances occur at integer harmonics of orbital frequencies but, if the wave amplitude is large enough, sub-harmonics can also be resonant [2].

 

Global modes can cause convective losses of resonant fast ions [3]. In contrast,  if fast ions resonate with many Alfv´en modes, stochastic transport occurs and the fast-ion profile flattens over the affected region [4]. In this regime, the fast-ion transport appears to be stiff and a critical gradient model can describe the fast-ion profile [5]. For a non-resonant ion, energy gained (or lost) during one phase of the wave is returned to the wave in the opposite phase. Sub-diffusive transport of non-resonant ions after one-half wave period is measured [6]. However, if a nonresonant fast ion crosses a loss boundary before the wave phase reverses, the energy is not returned to the wave. Alfv´en waves in the DIII-D tokamak cause losses of non-resonant fast ions [7]. Even though these Alfv´en modes are low-frequency, low-amplitude waves, they cause modification of the magnetic moment   [8].

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[1] Shu Zhou et al., Phys. Plasmas 19 (2012) 055904.

[2] G.J. Kramer et al., Phys. Rev. Lett. 109 (2012) 035003.

[3] W.W. Heidbrink et al., Plasma Phys. Cont. Fusion 53 (2011) 085028.

[4] R.B. White et al., Plasma Phys. Cont. Fusion 52 (2010) 045012.

[5] W.W. Heidbrink et al., The effect of the fast-ion profile on Alfv´en eigenmode

stability, Nucl. Fusion 53 (2013) submitted.

[6] Shu Zhou et al. Phys. Plasmas 18 (2011) 082104.

[7] Xi Chen et al., Phys. Rev. Lett. 111 (2013) 065004.

[8] G.J. Kramer et al., in preparation.

 

In collaboration with the DIII-D Energetic Particle group and with participants in the LAPD fast-ion campaign.