Frequencies of the geodesic acoustic mode and Alfvén gap modes in high-q2β plasmas with non-circular cross section

Fesenyuk, O. P.; Kolesnichenko, Ya. I.; Yakovenko, Yu. V.

doi:10.1063/1.4846816

Cited by 10 publications

(19 citation statements)

References 26 publications

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“…Without the elongation correction, the GAM frequency at high q min reduces to that in [24,32]. The gradient induced frequency upshift ( ∇ f ) in f RSAE-min is from [1,26,27] with the additional correction for elongation to be the same as that for f GAM (see equation (11) in [31]). Note, we are ignoring contributions from the density gradient due to the fact that they are relatively small in the L-mode discharges presented here.…”

Section: Model For Rsae Frequency Evolutionmentioning

confidence: 99%

“…The expressions for the TAE and GAM frequencies are modified from the standard cylindrical plasma expressions to include the effects of elongation and are adapted from [31] (also discussed in [55]) using…”

Section: Model For Rsae Frequency Evolutionmentioning

confidence: 99%

“…Of particular importance to the work presented here is the fact that the RSAE can be significantly modified by finite pressure effects and geodesic curvature which precludes the shear Alfvén wave continuum from going to zero frequency at a rational surface. Instead, the continuum is bounded by that of the geodesic acoustic mode [18] ( f GAM ) and the RSAE minimum frequency ( f RSAE-min ) lies above the local continuum tip at q min by an amount that depends on the local pressure as well as gradients in the local thermal and fast ion pressures [23][24][25][26][27][28][29][30][31]. ECH directly modifies the local electron temperature and temperature gradient and, in this way, can easily modify RSAEs as well.…”

Section: Introductionmentioning

confidence: 99%

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Electron cyclotron heating can drastically alter reversed shear Alfvén eigenmode activity in DIII-D through finite pressure effects

et al. 2016

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A recent DIII-D experiment investigating the impact of electron cyclotron heating (ECH) on neutral beam driven reversed shear Alfvén eigenmode (RSAE) activity is presented. The experiment includes variations of ECH injection location and timing, current ramp rate, beam injection geometry (on/off-axis), and neutral beam power. Essentially all variations carried out in this experiment were observed to change the impact of ECH on AE activity significantly. In some cases, RSAEs were observed to be enhanced with ECH near the off-axis minimum in magnetic safety factor (q min ), in contrast to the original DIII-D experiments where the modes were absent when ECH was deposited near q min . It is found that during intervals when the geodesic acoustic mode (GAM) frequency at q min is elevated and the calculated RSAE minimum frequency, including contributions from thermal plasma gradients, is very near or above the nominal TAE frequency ( f TAE ), RSAE activity is not observed or RSAEs with a much reduced frequency sweep range are found. This condition is primarily brought about by ECH modification of the local electron temperature (T e ) which can raise both the local T e at q min as well as its gradient. A q-evolution model that incorporates this reduction in RSAE frequency sweep range is in agreement with the observed spectra and appears to capture the relative balance of TAE or RSAE-like modes throughout the current ramp phase of over 38 DIII-D discharges. Detailed ideal MHD calculations using the NOVA code show both modification of plasma pressure and pressure gradient at q min play an important role in modifying the RSAE activity. Analysis of the ECH injection near the q min case where no frequency sweeping RSAEs are observed shows the typical RSAE is no longer an eigenmode of the system. What remains is an eigenmode with poloidal harmonic content reminiscent of the standard RSAE, but absent of the typical frequency sweeping behavior. The remaining eigenmode is also often strongly coupled to gap TAEs. Analysis with the non-perturbative gyro fluid code TAEFL confirms this change in RSAE activity and also shows a large drop in the resultant mode growth rates.Nuclear Fusion

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Section: Model For Rsae Frequency Evolutionmentioning

confidence: 99%

Section: Model For Rsae Frequency Evolutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electron cyclotron heating can drastically alter reversed shear Alfvén eigenmode activity in DIII-D through finite pressure effects

et al. 2016

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“…We will consider only | | V 10 (because | | − V 1,0 is the same). The contribution of the transversal component to this matrix elements (which we denote | | ⊥ V 10 ) comes mainly from the (m, n) = (0, 0) harmonic of the wave potential (it follows from the consideration in [26] that the β Φ ∼ Φ q 20 2 00 is small even when the plasma cross-section is elongated; here and below the subscript 'mn' at a quantity refers to the (m, n) Fourier harmonic of the perturbation). We obtain from (A.10): To calculate the integral appearing in (A.29), we notice that when ρ r / 1 and ε 1, the unperturbed motion of the passing particles is reduced to the pendulum Hamiltonian: [27], we obtain …”

Section: The Circle Approximates the Fast-ion Birth Velocity (ˆ∥mentioning

confidence: 99%

“…This approximation was used in our basic equation for the fusion reaction rate given by equation (26). In order to evaluate its accuracy, below we calculate the local fusion reaction rate, assuming that a plasma with Maxwell distribution function moves with the average velocity V, where T is the plasma temperature, M p is the plasma ion mass.…”

Section: Appendix a Hamiltonian Approach To The Study Of Motion Of Pmentioning

confidence: 99%

Manifestations of the geodesic acoustic mode driven by energetic ions in tokamaks

Kolesnichenko

Lutsenko

Yakovenko

et al. 2016

Plasma Phys. Control. Fusion

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Effects of the energetic-ion-driven Geodesic Acoustic modes (GAM and E-GAM) on the toroidally passing energetic ions and the concomitant change of the neutron yield of beam-plasma fusion reactions in tokamaks are considered. It is shown that due to large perturbations of the plasma density, the resonant energetic ions driving the instability can be considerably slowed down for a few tens of the particle transit periods, which is much less than the collisional slowing down time. The time of the collisionless slowing down is actually determined by the period of the particle motion within the resonance island arising because of the GAM / E-GAM. Being trapped in the island, the resonant particles can not only lose their energy but also gain it. One more effect of GAMs is the flattening on the distribution function of the resonant particles. Due to conservation of the canonical angular momentum during a GAM / E-GAM instability, the change of the particle energy is accompanied by a radial displacement of the resonant particle for a distance up to the poloidal Larmor radius of energetic ions. The particles are displaced inwards or outwards, depending on the direction of their motion along the magnetic field. Expressions describing the change of the neutron yield due to GAM modes are derived. It is found that the distortion of the velocity distribution of the resonant particles can lead to a considerable drop of the neutron emission even when effects of the particle radial displacement are small. The developed theory is applied to an E-GAM experiment on the DIII-D tokamak. Relations for the period of the motion within the resonance island of passing (both well passing and marginally passing) particles and the width of the resonance of the energetic particles with GAM modes and low-frequency Alfvén modes are derived.

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Electromagnetic effect on geodesic acoustic mode with adiabatic electrons

Huang

Ren

2019

Physics of Plasmas

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The geodesic acoustic mode (GAM) is analytically investigated by taking into account the finite-orbit-width (FOW) resonance effect to the second order and the finite β effect. The general dispersion relation is derived from the gyro-kinetic equations in the presence of nonzero δA∥, the parallel component of the perturbed magnetic vector potential. Transparent and concise expressions for the GAM frequency and Landau damping rate in the presence of the second order FOW effect and finite β effect are first presented. It is clearly shown that the m = ±2 harmonics dominant δA∥ and the kinetic expression of δA∥ have the same form as the fluid one. For the real frequency, the electromagnetic effect introduces a term on the order of q2β, which is comparable to the second order electrostatic terms, namely, the terms introduced by the second order FOW resonance effect. While for the collisionless damping rate, δA∥ does not directly introduce β–dependent terms, but affects the damping rate via modifying the real frequency. Besides, our analytical result shows good agreement with the numerical examinations.

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Frequencies of the geodesic acoustic mode and Alfvén gap modes in high-q2β plasmas with non-circular cross section

Cited by 10 publications

References 26 publications

Electron cyclotron heating can drastically alter reversed shear Alfvén eigenmode activity in DIII-D through finite pressure effects

Electron cyclotron heating can drastically alter reversed shear Alfvén eigenmode activity in DIII-D through finite pressure effects

Manifestations of the geodesic acoustic mode driven by energetic ions in tokamaks

Electromagnetic effect on geodesic acoustic mode with adiabatic electrons

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