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Research Highlight E.V. Belova, et al. Schedule of Burning Plasma Events Contact and Contribution Information
Energetic Particles Topical Group, Leaders: D.C. Pace and N.N. Gorelenkov
This month’s highlight by E.V. Belova, et al., proposes an energy channeling mechanism to explain flattening of the electron temperature profiles at high beam power in plasmas at the National Spherical Torus Experiment (NSTX). Self-consistent simulations of neutral-beam-driven compressional Alfvén eigenmodes (CAEs) in NSTX demonstrate strong coupling of CAEs to the kinetic Alfvén wave at the Alfvén resonance location. The results from this work may be important for explaining, and predicting, scenarios of lower performance in tokamaks.
Coupling of Ion-beam-driven Compressional Alfvén Eigenmodes to Kinetic Alfvén Waves and the Resultant Channeling of Beam Energy Away from the Center in NSTX
E.V. Belova1, N.N. Gorelenkov1, N.A. Crocker2, E.D. Fredrickson1, K. Tritz3
1 Princeton Plasma Physics Laboratory, Princeton, NJ 08540, USA
2 University of California, Los Angeles, CA 90095, USA
3 Johns Hopkins University, Baltimore, MD 21218, USA
Flattening of electron temperature profiles and anomalously low central temperature at high beam power in the National Spherical Torus Experiment (NSTX) have been linked with strong activity of Alfvén modes in a sub-cyclotron frequency range . The reduced heating of the plasma core in NSTX can significantly limit plasma performance, and potentially can have important implications for future fusion devices, especially low aspect ratio tokamaks. Modes in a sub-cyclotron frequency range are often observed during neutral beam injection in NSTX, and they were identified as compressional Alfvén eigenmodes (CAEs) and global Alfvén eigenmodes (GAEs). These are driven unstable through resonances with the super Alfvénic beam ions [2,3]. Previous theoretical studies attributed flattening of the electron temperature profile to an enhanced electron transport caused by these modes . Other estimates, however, suggest that Alfvén eigenmode-induced transport should have a minor effect, but the energy channeling from center-localized GAEs to continuum damping closer to the edge can be responsible for the observed flattening of the electron temperature profiles .
We have performed the first self-consistent simulations of neutral-beam-driven compressional Alfvén eigenmodes demonstrating an important alternative, i.e., an energy channeling mechanism that will occur for any unstable CAE in NSTX. Three-dimensional hybrid MHD-particle simulations show that an essential feature of CAEs in toroidal geometry is their coupling to kinetic Alfvén waves (KAW) at the Alfvén resonance location. It is demonstrated that the beam-driven CAE can mode-convert to KAW, channeling energy from the beam ions at the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. This mechanism can explain the reduced heating of the plasma center in NSTX. It is also shown that strong CAE/KAW coupling follows from the dispersion relation, and will occur for any unstable compressional mode in NSTX or other toroidal devices. Thus it is important for predictive modeling of spherical tokamak (ST) plasmas and tokamaks in general.
Figure 1: Simulation of the beam-driven compressional Alfvén modes in the NSTX. Contour plots of magnetic field perturbation for n = 8 (a) and n = 4 (b) CAE modes show resonant coupling to KAW. Solid contour line on |δB⊥| plots corresponds to the resonant condition ωA(Z, R) = ω.
The hybrid code HYM  has been used to investigate properties of beam ion driven compressional Alfvén modes for the high confinement-regime plasma of NSTX shot 141398. Equilibrium profiles and plasma parameters have been chosen to match magnetic field and plasma profiles for this shot. The plasma was heated by 6 MW of 90 keV Deuterium beams with ne = 6.7 × 1019 m–3, Bt = 0.325 T, Ip = 0.8 MA, nbeam = 3.5 × 1018 m−3 and vbeam = 4.9VA, where VA is the Alfvén velocity. In this shot, significant Alfvén mode activity has been observed, and detailed measurements of amplitudes and mode structures were obtained . The HYM code is a 3D nonlinear, global stability code in toroidal geometry, which treats the beam ions using full-orbit, delta-f particle simulations, while the one-fluid resistive MHD model is used to represent the background plasma. Simulations for this case show that most unstable modes for toroidal mode numbers n = 5 − 7 are GAEs. The most unstable modes for n = 4 and n = 8, 9 are CAEs, which have been identified based on the large compressional component of perturbed magnetic field. The calculated range of the unstable toroidal mode numbers, frequencies, and mode polarizations appear to be reasonably close to experimental observations . Figure 1 shows poloidal contour plots of the perturbed magnetic field for the n = 8 (ω = 0.48ωci) and the n = 4 (ω = 0.35ωci) CAEs. It can be seen that the CAEs are localized near the magnetic axis, where they have mostly compressional polarization, and δB∥ is significantly larger than δB⊥ everywhere, except in the radially localized region on the high-field-side where the resonant condition ωA(Z,R) = ω is satisfied (ωA(Z,R) = nVA/R is the local Alfvén frequency, and ω is the frequency of the CAE mode in the simulation). Simulations for both low-n and high-n CAEs show resonant coupling to the kinetic Alfvén wave.
Figure 2: Radial component of the Poynting vector S⃗R = ⟨E⃗ × B⃗⟩ from nonlinear simulations of the n = 4 beam-ion-driven compressional Alfvén eigenmode (CAE) in NSTX.
Figure 2 shows the radial profile of the radial component of the ￼Poynting vector S⃗R = ⟨E⃗ × B⃗⟩R obtained from the self-consistent nonlinear simujlations of the n = 4 CAE mode near saturation. It is seen that the energy flux is directed away from the magnetic axis (CAE) towards the Alfvén resonance location (KAW). Calculated change of the energy flux across the resonant layer at R = 0.6 - 0.7 m is 1.5 × 105 W/m2, and estimating surface area as ~2–3m2, the power absorption can be calculated as 0.3-0.5 MW, which is a significant fraction of the beam power. The saturation amplitude of the n = 4 CAE instability in the simulations is δB∥/B0 = 6.6 × 10-3, which is comparable to values obtained through analysis of the experimental data in this plasma. Thus, measured plasma displacement |ξ| = 0.1 − 0.4 mm  corresponds to δB/B0 = (0.9 - 3.4) × 10-3. It is also useful to estimate a fraction of beam power which can be transferred to CAE as P = 2γ ∫(δB)2/4πd3x, where γ is the growth rate of the CAE. For γ/ωci = 0.005 − 0.01, and experimentally measured amplitudes, it gives P = 0.013 − 0.4 MW, comparable to absorption rate obtained in nonlinear simulations. Calculated power absorption is significant enough to have a direct effect on the electron temperature profile.
In summary, it is found that beam-driven compressional Alfvén modes in NSTX mode-convert to KAWs, and therefore can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. This mechanism can provide alternative explanation to the observed reduced heating of the plasma core in the NSTX. Future work will include the detailed study of the conditions of the GAE and CAE instabilities, and comparison of the relative importance of the energy channeling and anomalous electron transport mechanisms. This work was accepted for poster presentation at the 2014 IAEA Meeting (Saint-Petersburg, Russia) and an invited presentation at the 2014 APS Division of Plasma Physics meeting (New Orleans, LA), and a paper has been submitted to Physical Review Letters.
The simulations reported here were carried out using resources of the National Energy Research Scientific Computing Center (NERSC). This research was supported by the U.S. Department of Energy (NSTX contract # DE-AC02-09CH11466).
D. Stutman, et al., Phys. Rev. Lett. 102, 115002 (2009)
 E.D. Fredrickson, et al., Phys. Rev. Lett. 87, 145001 (2001)
 N.A. Crocker, et al., Nucl. Fusion 53, 043017 (2013)
 N.N. Gorelenkov, et al., Nucl. Fusion 50, 084012 (2010)
 Ya.I. Kolesnichenko, Yu.V. Yakovenko, and V.V. Lutsenko, Phys. Rev. Lett. 104, 075001 (2010)
 E.V. Belova, et al., Phys. Plasmas 7, 4996 (2000)
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|April 28 – May 1, US/EU Transport Task Force Workshop, Salem, MA, United States|
|May 4–6, FES Workshop: Plasma-Materials Interactions, Princeton, NJ, United States|
|May 5–7, ITPA: Transport and Confinement Topical Group Meeting, ITER Headquarters, France|
|May 18–22, 15th International Conference on Plasma-facing Materials and Components for Fusion Applications, Aix-en-Provence, France|
|May 19–23, ITPA Diagnostics Topical Group Meeting, NIFS, Japan|
|May 20, DEADLINE for submission of manuscripts to the Journal of Fusion Energy Special Issue on Strategic Opportunities|
|May 24–28, 42nd IEEE International Conference on Plasma Science (ICOPS), Belek, Antalya, Turkey|
|May 27, DEADLINE for submission of abstracts and related materials to attend the IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems|
|June 2–4, FES Workshop: Integrated Simulations for Magnetic Fusion Energy Sciences, Washington, D.C.|
|June 22–26, 42nd EPS Conference on Plasma Physics, Lisbon, Portugal|
|August 24 – September 4, 2th Carolus Magnus Summer School on Plasma and Fusion Energy Physics|
|September 1–4, IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems, Vienna, Austria|
|September 7–9, ITPA: Energetic Particles Topical Group Meeting, Vienna, Austria|
|September 14–18, 12th International Symposium on Fusion Nuclear Technology, Jeju Island, South Korea|
|November 16–20, 57th APS Division of Plasma Physics Meeting, Savannah, GA, United States|
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