THE DIFFUSION OF FAST IONS IN OHMIC TFTR DISCHARGES

Short duration (20 msec) neutral deuterium beams are injected into the TFTR tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1986 (IAEA, Vienna, 1987), Vol. I, p. 5 11. The subsequent confinement, thermalization, and diffusion of the beam ions are studied with multichannel neutron and charge exchange diagnostics. The central fast-ion diffusion ( co.05 m2/sec) is an order of magnitude smaller than typical thermal transport coefficients.


I. INTRODUCTION
Two requirements for an ignited D-T fusion reactor are sufficient energy confinement of the thermal plasma and confinement of fusion-product alphas while they thermalize. Measurements of the diffusion of ions injected by neutral beams relate to both thermal confinement and alpha confinement. First, experimental thermal transport coefficients are generally inferred by assuming that the energetic ions that heat the plasma undergo no diffusion during thermalization. If this assumption has been incorrect, the inferred ion and electron thermal diffusivity profiles are erroneous, with consequent implications for theories of tokamak transport. Second, comparisons of fast-ion diffusion with thermal diffusion are useful in assessing the mechanisms responsible for anomalous thermal transport. Finally, beam-ion diffusion is relevant to fusion-product diffusion, because both beam ions and fusion products are characterized by gyroradii pr that are large compared to the thermal gyroradius pi.
Although neoclassical fast-ion behavior in tokamaks is widely assumed, the experimental evidence supporting this assumption is scanty. Classical thermal&&ion of beam ions was verified to 25% accuracy on DID-D,' but radial transport was not studied. Measurements of ripple-trapped beam ions in TFR suggested some anomalous transport,2 as did charge-exchange measurements on ISX-B.3 Many other experiments found behavior roughly consistent with neoclassical transport, but the only quantitative bound on central beam-ion transport in the literature4 is D 5 0.5 m2/sec. The most accurate previous study of beam-ion transport' established that the inward diffusion of a ring of toroidally "passing" beam ions in the outer region of TFTR6 (r> 0.35 m) was smaller than 0.05 m2/sec; however, this study did not address radial transport from the plasma center (where fast ions are generally created). In this paper, the bound on cen-*) Permanent address: Department of Physics, University of California, Irvine, California 92717. b, Permanent address: Los Alamos National Laboratory, Los Alamos, New Mexico 87545. ') Permanent address: Naka-machi, Naka-gun, Ibaraki-ken 31 l-01, Japan. tral beam-ion transport is lowered an order of magnitude to D 5 0.05 m2/sec, establishing for the first time that the central transport is comparable to neoclassical predictions.

II. EXPERIMENT
The experimental technique is an extension of the short beam pulse experiments developed on Doublet III and DIII-D. ' The basic idea of the experiment is to create a known beam-ion distribution and then observe its evolution in a well-diagnosed background plasma. Short ( -20 msec), intense ( 5 20 MW) pulses of deuterium neutral beams ( 83-96 kV) are injected into the steady-state portion of Ohmically heated, deuterium TFTR plasmas. The ions are injected with roughly equal amounts parallel and antiparallel to the plasma current at angles that have a minimum major radius between R,, = 1.73 and 2.32 m. Since the beam pulse is short compared to the beam-ion deceleration time ' (vg ' -420 msec), the velocity distribution of the beam ions at the end of the pulse is essentially that of the injected neutrals, i.e., -48% (by particle fraction) at 83-96 kV, -28% at 42-48 kV, and -25% at 28-32 kV. The initial spatial distribution of the beam is checked by comparing measurements of the neutron emission with calculations of the expected deposition profile. As expected, the deposition peaks strongly on axis (Fig. 1) . The electron temperature is measured with electron cyclotron emission diagnostics* and the electron density is measured by inversion of ten-channel interferometer data;' both diagnostics have been compared extensively with Thomson scattering measurements" and have an absolute error of 5 10%. The plasma effective charge Z,, and deuterium density are inferred from tangential profiles of the visible bremsstrahlung emission." Following the beam pulse, the central electron temperature decreases slightly ( -7%)) the line-average electron density increases by -15%, the central Z,, varies less than 5%, and the ion temperature and total pressure approximately double. Thus, the 100-250 kJ beam pulse constitutes a relatively minor perturbation to the electrons but a major perturbation to the ions. For all but one of the seven conditions studied, the calculated neutron source strength at the end of the beam pulse agrees to within 15% with the measured neutron emission (absolutely calibrated to f 13%),i2 confirming that MAJOR RADIUS (m) FIG. 1. Profile of the line-integrated 2.5 MeV neutron flux measured by the multichannel neutron collimatori for the 32 msec immediately following the beam pulse. Twenty-four similar pulses are added to improve counting statistics. The profile agrees well with the profile computed by the TRANSP code" for a single representative pulse. the initial beam and plasma characteristics are correctly measured and modeled.
The subsequent evolution of the beam population is inferred from neutron and charge-exchange measurements. The total 2.5 MeV neutron emission is measured by a set of fission detectors." Calculations indicate that the signal is 60% beam-target reactions and 40% beam-beam reactions for the conditions of Fig. 1. The profile of the neutron emission is measured by ten vertically viewing, collimated neutron detectors.r3 The steep radial profile ( Fig. 1) requires that multiple pulses ( 1-3 per shot) over many shots (4-10) are added to improve counting statistics in the outer channels. The dominant uncertainty in the neutron profile is associated with neutrons that backscatter off of machine components into neighboring channels. Specially formed, small minor radius plasmas are used to determine the scattering correction to the measured signals.'4 After corrections for scattering, the integral of the neutron profile agrees (within 20% uncertainty) with the measurements of the total neutron emission.15 The third diagnostic system is a pair of vertically viewing E llB neutral-particle analyzers located at R = 2.44 and 2.97 rn.16 The contribution of scattered light is measured by three anodes above the injection energy and subtracted from the measured signals to obtain the actual neutral flux. Passive charge exchange is employed so that the measured chord-integrated signal is more heavily weighted toward the plasma edge than the neutron measurements, which are strongly weighted to the plasma core. A major difference between the charge-exchange and neutron diagnostics is that the charge-exchange diagnostics measure only banana-trapped ions, while the neutron signals are dominated by the toroidally circulating ion population.
The response of these diagnostics to a beam pulse at 3.0 set is shown in Fig. 2. Since the fusion cross section decreases with decreasing energy, the 'neutron source strength falls as the beam ions decelerate [ Fig. 2(a)   The expected behavior of the signals for various diffusion coefficients is calculated using the TRANSP" code. Experimental inputs to the code include the neutral beam parameters, the electr'm temperature and density, the visible bremsstrahlung signal, and magnetics data (for the plasma shape). With these experimental inputs, the code calculates beam deposition, deceleration, and pitch-angle scattering using the classical formulas (with a typical accuracy of -f 9% in the slowing-down time due to the experimental uncertainties). The evolution of the beam distribution can be calculated by a Monte Carlo technique" or by a Fokker-Planck treatment, l8 The two techniques typically agree to within 5% for calculations of the rate of decay of the neutron source strength. An empirical, spatially constant, beam diffusion coefficient may be incorporated in the calculations. After the beam distribution is calculated, the expected signals are computed for the various diagnostics. In the calculation of the charge-exchange signals, the neutral density is assumed poloidally and toroidally symmetric with a timeevolving magnitude that is consistent with the measured poloidally averaged D, signal. l9 The edge D, signals at various poloidal positions increase from 20% to 80% in response to a beam pulse, but the shape of the neutral profile is not calculated to change while the beam population evolves. Since the charge-exchange sight lines do not intersect the path of the neutral beams and the limiter is the toroidally symmetric inner wall, the assumption of toroidal symmetry is reasonable for these plasmas.
The predicted decay in total neutron emission and central neutron emission becomes faster as the diffusion coefficient D increases [Figs. 2 (a) and 2 (d) 1, because the fast-ion population, initially strongly peaked at the center, diffuses outward in minor radius to regions of shorter thermalization time. Off axis, the predicted decay rate only becomes shorter for large values of D, since transport from the plasma center balances outward losses [ Fig. 2 ( [The difference between the D = 0 prediction and experiment is within experimental error ( -10%) and may be caused by a slight overestimate of the central density.] The off-axis signals require diffusion of order 0.1 m*/sec to match the experiment [Figs. 2(c) and 2 ( f) 1. Perhaps large-angle scattering, which is neglected in our Fokker-Planck calculations, increases energy diffusion (resulting in a slower central decay rate) and increases pitch-angle scattering (giving a larger off-axis charge-exchange signal). Alternatively, the true diffusion coefficient may increase with radius. In any event, the data indicate that the average beam-ion diffusion is less than 0.1 m*/sec. This conclusion is consistent with the data from other Ohmic discharge conditions with I, = 0.8-1.6 MA, B, = 3.1-4.1 T, R, = 2.42-2.60 m, and ?I, = 0.7-2.0X lOi m -3 (Fig. 3). In particular, a plasma condition with a large m = 4, n = 1 nonrotating, ("locked") mode and one with an out-shifted magnetic axis (to enhance ripple losses) are included. Discharges where beam-beam reactions are calculated to predominate exhibit behavior similar to the discharges dominated by beam-target reactions. No systematic differences in fast-ion behavior between these conditions and the baseline condition (Fig. 2) are observed. Assuming that the same transport processes are operative in all of the discharges, the total neutron emission and central charge-ex- 3169 Phys

III. DISCUSSION
Typical TFTR diffusion coefficients and thermal diffu-sivities5,*' are -1 .O m*/sec. For example, in the discharge of Fig. 2, the electron thermal diffusivity at r/a-O.3 is approximately X, 2 0.5 m*/sec. This value is an order of magnitude larger than our bound on the beam-ion diffusion coefficient D. A likely explanation for the difference between thermal transport and fast-ion transport is that beam ions do not stay in resonance with the fluctuations responsible for thermal transport since their drift orbit displacements exceed the radial correlation length A, of the fluctuations.5'2' (A similar process may account for enhanced high-energy runaway electron confinement.*' ) If one assumes that this explanation is correct, then the observed ratio of D /xe implies that the fluctuations responsible for transport have a radial scale length significantly smaller thanpf-1 cm. In contrast to the thermal transport (which is far in excess of neoclassical expectations), the central beam-ion diffusion coefficient is consistent with the diffusion predicted by neoclassical theory [D-0( 0.01 m*/sec) 1. (The neoclassical pinch velocity is negligible.) The diffusion of off-axis banana-trapped ions does exceed the neoclassical prediction, however.
The sawtooth instability has been observed to transport fast ions+** For the condition documented in Fig. 2, the drop in central electron temperature at a sawtooth crash is only AT,/T, = 14% and the inversion radius is only 0.13 m with an 18 msec period. Thus a relatively modest effect is expected. Another possible transport mechanism is associated with toroidal field ripple. The absence of perfect toroidal symmetry causes fast ions trapped in the l/R field wells to suffer a small radiaI displacement at each poloidal half-orbit. For the plasma conditions of these experiments, either pitch-angle scattering or the finite radial excursions themselves are sufficient to decorrelate successive radial steps over most of the plasma, leading to radial diffusion. The expected "rippleplateau" diffusivity23 is strongly dependent on fast-ion energy (Da E 3'2) and on the magnitude of the toroidal field ripple. Since few beam ions are born on banana orbits (only neutrals ionized outside R~3.05 m are initially trapped), only the charge-exchange measurements are sensitive to ripple transport. For plasmas centered at R = 2.42 m, the calculated ripple transport is very small [e.g., D(E = 90 keV) -0.01 m"/sec at R = 2.5 m, z = 0.3 m], which is consistent with the absence ofobservable diffusion in the central charge-exchange signal [ Fig. 3 (b) ] . The expected ripple transport increases rapidly with increasing major radius. For example, at R = 3.0 m and z = 0.3 m the expected diffusion of 90 keV ions due to field ripple is D( E = 90 keV) -1 .O m*/sec. In our simulations, the data from the charge-exchange detector at R = 2.97 m are consistent with a spatially averaged diffusion coefficient of -0.1 m*/sec [ Fig. 3 (d ) 1. Thus it seems likely that ripple transport affects the signal measured by this detector.
In conclusion, in low-beta TFTR plasmas (/?, 5 0.2%) with small beam-ion concentrations (nb/ne 5 10%) the deceleration rate ofbeam ions agrees well with classical theory, as it did in DIII-D. ' The agreement of the volume-integrated neutron source strength with the simulations indicates that the central fast-ion diffusion coefficient is much less than 0.1 m*/sec, which is much smaller than thermal transport coefficients. Thus a key assumption of conventional transport analysis (that beam-ion behavior is classical) is validated, as are the transport simulations of the initial beam deposition. It should be noted, however, that more intense beam populations could modify the fluctuation spectrum in a manner that increases fast-ion transport, Future work will investigate beam-ion transport during strong auxiliary heating. The difference between D andx, suggests that microturbulence with decorrelation lengths smaller than 1 cm are responsible for thermal transport. Finally, the small beamion diffusion suggests that, in the absence of collective fastion driven instabilities, alphas in a reactor will thermalize more rapidly than they will be lost.