Search for alpha driven BAEs in TFTR

A search for alpha driven beta-induced Alfven eigenmodes (BAEs) was conducted in low current (1.0-1.6 MA) TFTR supershots. Stable high beta deuterium-tritium (DT) discharges were obtained with beta p=2.4 and a central alpha beta of 0.1%. Instabilities between 75 and 200 kHz were observed by magnetics probes in many DT discharges, but the activity was also present in deuterium-deuterium (DD) comparison discharges, indicating that these modes are not destabilized (principally) by the alpha particle population. Losses of fusion products are also similar in the two sets of discharges. Theoretical simulations confirm that the achieved alpha particle pressure is too small to produce instability


INTRODUCTION
Alpha particles are produced in DT fusion reactions. In a tokamak reactor, intense alpha populations might drive instabilities that cause anomalous transport of the alpha particles, resulting in degraded plasma performance or damage to internal vacuum vessel hardware. It is important, therefore, to determine the stability threshold of alpha driven instabilities.
In DIII-D experiments that are designed to simulate alpha particle effects, intense beam ion populations destabilize two types of AlfvCn instability, the toroidicity-induced AlfvCn eigenmode (TAE) [ 11 and the beta-induced AlfvCn eigenmode (BAE) [2]. The BAEs have frequencies that arc -40% of the TAE frequency [2] (in a low frequency gap beneath the Alfv6n continuum of ideal MHD [3]). BAEs occur in high beta plasmas. They were first observed in plasmas where the fast ion speed was comparable to the AlfvCn speed, but were later observed in plasmas with sub-AlfvCnic fast ion populations [4].
Motivated by these simulation experiments, we tried to destabilize BAEs with alpha particles in TFTR. At the time of the experiment there were no theoretical predictions of BAE stability, so we adopted an empirical approach. Our operational goal was to maximize the alpha particle pressure (to maximize the instability drive) at a large value of poloidal beta (to maximize the low frequency gap in the AlfvCn continuum). No alpha driven BAEs were observed.
Since the time of the experiment, more has been learned about instabilities in the BAE gap. Experimental work on TFTR found that instabilities in this band have frequencies comparable to 0*~i/2 [5] is the ion diamagnetic frequency), as expected for kinetic ballooning modes (KBMs) [6]. Numerical studies [7-91 discovered energetic particle modes (modes that do not exist in the absence of a fast ion population) with frequencies . similar to the 'BAEs' observed in DIII-D. A recent unified theoretical treatment of the background plasma behaviour (in the absence of energetic particles) found that the most unstable regime corresponds to a coupling N U C L E A R F U S I O N , Vol. 36, No. 12 (1996) HEIDBRINK et ai.

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between the drift-like KBM branch and the AlfvCnic BAE branch [lo]. Detailed comparisons of these new theories with the beam driven DIII-D and TFTR instabilities will be the topic of a future paper. This paper addresses the effect of alpha particles on modes in this BAEIKBM frequency band.

EXPERIMENT
The data were obtained during a week of TFTR operation in April 1995. The plasmas were limited on a well conditioned inner wall (major radius R = 2.52 m, minor radius a = 0.87 cm) and the confinement was characteristic of supershots [ 1 13 (typically T~ = 0.16 s). Approximately equal numbers of deuterium and tritium neutral sources were injected into nineteen 'DT' discharges; an additional 140 'DD' discharges with deuterium injection alone comprise the remainder of the dataset. The operational strategy had four steps. disruption for an alpha particle slowing-down time yields a maximal value of 0, in subsequent DT shots.) (b) After reconditioning the walls, produce approximately ten DD discharges with N, -1 sources to reestablish reproducibility.
(c) Convert half of the neutral beams to tritium and produce a DT discharge with N, sources.
(d) Produce a DD comparison discharge with N, or N, + 1 sources.
The beam power varied from 5 to 22 MW, the beam voltage was typically 100 keV and a similar neutral beam power was injected both parallel and antiparallel to the plasma current ('balanced' injection). Plasmas with toroidal fields BT of 3.3, 4.7 and 5.1 T and currents Zp between 0.7 and 1.6 MA were produced. Relative to other TFTR DT discharges, the distinctive feature of these experiments is the use of a low, steady plasma current. Figure 1 compares the best 1.0 MA discharge with a 2.5 MA discharge that had a large value of 0, [12]. Since the maximum pressure in TFTR supershots is governed by a central beta limit that scales with the normalized current ZplaBT, the maximum beam power in our low current discharges is about The equilibrium is computed by EFIT [19] using magnotics data, motional Stark effect (MSE) PO] measurements and kinetics profiles from TRANSP; the EFIT q projZe is also shown. The Doppler shift correction uses toroidal rotation and temperature proJiles measured by charge exchange recombination spectroscopy (1 71, and the mass density and KBM profiles are obtainedfrom TRANSP (Fig. 2). The abscissa is the normalized poloidal jlux. NUCLEAR FUSION, Vol. 36, No. 12 (1996) half as large as that in high current supershots (Fig. 1). The stored energy W is also -50% smaller, so the fusion reaction rate is only about a third of the high current value. Since disruptions were delayed until the alpha pressure had peaked, the resulting central alpha beta is also about a third of the high current value (Fig. 1). On the other hand, the low current discharge has a relatively large beta limit for TFTR (product of normalized beta and density peaking factor PNn,(0)l ( n e > = 6 . 8 ) , so the poloidal beta is -3 times larger than that in high current supershots (Fig. 1).
As is typical for supershots, the spatial profiles peak strongly at the magnetic axis (Fig. 2). The density is relatively low and the beam fuelling is strong, so the beam density is comparable to the thermal ion densities and the central beam pressure is a large fraction (-40%) of the total. The alpha pressure is an order of magnitude smaller. The large value of poloidal beta creates a relatively large low-frequency gap in the AlfvCn continuum (Fig. 3).
In addition to disruptions, three types of instability are observed in most of these high beta plasmas (Fig. 4).
In the low frequency band ( 5 50 kHz), modes with toroidal mode numbers n between 1 and 4 are observed In other cases, single modes with n = 1-5 appear in this frequency band.
Like the DIII-D BAEs, these intermediate frequency modes have frequencies that fall in the low frequency gap beneath the AlfvCn continuum of ideal MHD (Fig. 3). In a frame rotating with the plasma, all of the toroidal modes in a cluster have nearly the same frequency in the interior of the plasma. (In other words, the splitting of the peak into a 'cluster' is probably caused by the Doppler shift.) Calculations with the ideal MHD code GAT0 reveal global eigenmodes in the centre of the plasma with frequencies close to the measured frequency (Fig. 3). These eigenmodes resemble the theoretical 'BAEs' computed for DIII-D equilibria [25]. The internal frequency is also comparable to the expected frequency [6] of KBMs (Fig. 3).
Having established that these plasmas can support 'BAEs' similar to those observed in DIII-D, we proceed to an examination of the effect of alpha particles on the modes. Our approach is to compare DT discharges with companion DD discharges that have similar plasma parameters (Fig. 5). No effect correlated specifically with alpha particles is observed.
(a) A bank of bandpass filters analyses the fluctuations measured by a magnetic probe. The amplitude of the fluctuations is comparable in DT and DD comparison discharges in both the 75 to 95 kHz filter band and in the 100 to 150 kHz filter band. In addition, in DT discharges, the peak value of the magnetics signal does not necessarily coincide with the maximum value of the alpha density.
(b) Scintillators at three different poloidal locations (45, 60 and 90') measure fusion product losses. The temporal evolution of the signals is very similar in DT and DD discharges. The ,signals appear consistent with the expected evolution associated with prompt losses [27]. Little or no correlation with the magnetic fluctuations is observed. If anomalous losses occur, they are much smaller ( 5 10%) than the prompt losses.
(c) For a representative subset of the DT and DD discharges, coherent core fluctuations are not observed between 50 and 150 kHz by the reflectometer diagnostic [28], Signals from the electron cyclotron emission grating polychromator [15] are similar in DT and DD discharges.
(d) For discharge 85 863, the beam emission spectroscopy diagnostic [29] does not observe any coherent fluctuations above 50 kHz. This qualitative assessment is supported by a quantitative analysis of the magnetics and scintillator data. Measurements at 2 or 3 different times for every discharge in the dataset were entered into a database. If BAEs were destabilized by alpha particles, the mode amplitude at large pp should be larger in DT shots than in DD shots, but this is not observed for fluctuations between 100 and 150 kHz (Fig. 6). Similar results are obtained in the 75 to 95 kHz frequency band. The mode amplitude also does not correlate with the 14 MeV neutron emission (the alpha creation rate) SDT or with other plasma parameters (Zp, Ze, B T , W, TE, PB).
Similar results are obtained for the scintillator data. For all three detectors, the normalized signal (losdneutron) depends weakly on the magnetics amplitude and on Pp, SDT, Ip, ne, ne(0)l(n,>, BT, W, TE and PB.

COMPARISON WITH THEORY
The null result of this experiment is consistent with theoretical and empirical predictions.
Gyrokinetic-magnetohydrodynamic simulations [9] indicate that the alpha particle drive in the experiments is too weak to destabilize energetic particle modes and KBMs. The code computes the stability of high-n energetic particle modes and KBMs non-perturbatively in a local approximation. For the simulation, we select parameters near the maximum gradient of the alpha pressure at rla = 0.3 (normalized 9 = 0.2) for discharge 85 863. The alpha distribution function is taken as an isotropic slowing-down distribution of passing particles only. (Inclusion of trapped alphas has a minor effect on the computed stability threshold.) To isolate the effect of the alpha particles, the kinetic effects of beam ions are neglected in the simulation but the beam pressure is included in the MHD fluid core pressure.
The total pressure (alpha + core) is held fixed when the alpha pressure is varied. (In the experiment, the beam power was adjusted to keep the plasma near the beta limit .) For the parameters of the experiment, the core pressure places the plasma just above the marginal stability point for ideal high-n ballooning modes but finite effects stabilize the ideal modes (in the absence of energetic particles). An alpha particle drive of aE = -q2Rd&/dr = 0.027 gives instability ( Fig. 7(a)). The experimental value of aE is -40% of the predicted value. The predicted frequency of the mode is comparable to ( Fig. 7(b)), in rough agreement with the experimentally observed value. The agreement between experiment and theory should be viewed with caution, however, since the coupling between KBMs and betainduced AlfvCn eigenmodes due to the finite thermal ion temperature gradient (vi) [lo] is neglected in the simulation and, in addition, the high-n approximation is dubious for mode numbers of 2 to 4. In another TFTR experiment, alpha particle losses were correlated with 100 to 200 kHz MHD activity in a high current (2.1 MA) supershot plasma [30]. A theoretical analysis [30] suggests the modes are KBMs that are destabilized primarily by the background plasma pressure, with the alpha particles with @,(O) = 0.23% only making a small destabilizing contribution. Assuming that the general features of this analysis apply to our low current discharge, the 5 0.1 % 0, in our experiment is too small to excite KBMs, which is consistent with the conclusion of the gyrokinetic simulation.
These theoretical predictions are also consistent with empirical predictions. The threshold for beam driven BAEs in DIII-D is around (Ob ) 2 1 % [4], where (Ob) is the volume averaged beam beta. In the present experiment, the observed modes in the 50 to 150 kHz range are probably destabilized by the ions and by the plasma pressure. The beam beta is 0 (1 %), which is an order of magnitude larger than the alpha beta (Fig. 2(c)). Thus, in order to make a significant contribution to the instability drive, the alpha particles would have to resonate much more strongly with the BAEs than the beam ions do.
Empirical scaling based on TAE experiments in TFTR is also consistent with these expectations. In DIII-D, the stability threshold for the beam driven BAE is comparable to the stability threshold for the beam driven TAE [2]. So far, TAEs driven by alpha particles alone have not been observed in TFTR [31-331 (even in plasmas with -3 times larger alpha pressure than in our discharges). In one experiment [34], the minority ions created by ion cyclotron heating supplemented the instability drive produced by the alpha particles; estimates indicate that alpha particles with a central beta of 0.13% provided 10 to 30% of the drive needed to destabilize the TAE. If we assume that the alpha drive is proportional to 0, and make the rough approximation that the damping of the background plasma for the TAE experiment is comparable to the damping of BAEs in our experiment, the estimated alpha drive in our experiment is only -15% of the damping.
In summary, gyrokinetic simulations and empirical scaling based on previous DIII-D and TFTR experiments predict stability for the achieved conditions.

CONCLUSION
Any contribution of alpha particles to the destabilization of BAEs or KBMs in low current TFTR supershots is below the threshold of detection. The alpha particle drive appears to be an order of magnitude weaker than the drive associated with the beam ions and the background plasma.