Sawtooth mixing of alphas, knock on D, T ions and its influence on NPA spectra in ITER plasma F.S. Zaitsev 1, 4, N.N. Gorelenkov 2, M.P. Petrov 3, V.I. Afanasyev 3, M.I. Mironov 3 1 Scientific Research Institute of System Development, Russian Academy of Sciences 2 Princeton Plasma Physics Laboratory, Princeton University, USA 3 A.F. Ioffe Physical Technical Institute, St. Petersburg, Russia 4 Moscow State University, Russia
Introduction ITPA EP April 2017: ITER HQ stress use of diagnostics for plasma control and optimal performance rather than studying physics. An important direction of fusion research is studying effect of plasma instabilities and oscillations on fast ions behavior. Detailed information about such effects is essential for adequate interpretation of measurements, effective technology of fusion reaction maintenance and etc. Instabilities can lead to change in the plasma energy balance due to a significant radial redistribution of fast ions and their loss from plasma. One of the effective tools for fast particles diagnostics is NPA (Neutral Particle Analyzer), which gives direct observation of particles distribution. In this talk we consider sawtooth oscillations. Generalize B.B. Kadomtsev plasma mixing formula for relevant to ITER case. Apply code FPP-3D (Fokker-Planck Package Three-Dimensional) for studying possibility of detecting with NPA the ratio of D and T in ITER plasma and observing sawtooth oscillations. 2
Obtaining reliable results for ITER plasma is complicated by: Large deviation of fast ion trajectories from the flux surfaces. Coulomb interaction: friction and diffusion over speed, pitch-angle scattering, neoclassical radial transport and etc. Particle sources, such as alpha-particles He 4 source in D, T fusion. Particle losses, e.g. direct orbit losses from plasma. Nuclear elastic scattering (NES): charged particles with sufficiently high energy can approach other charged particles close enough for strong nuclear interactions with large energy exchange to occur. Plasma instabilities and oscillations, e.g. sawtooth. Ripple radial diffusion, if magnetic ripples are high enough. There is enhanced interest in the NES effect, because it gives big rise to D and T distributions at high energies, which can be measured with NPA. See, e.g. analyses of JET fusion pulses in par. 1.8.3.1, 4.4, 4.7 of [1] F.S. Zaitsev. Mathematical modeling of toroidal plasma evolution. English edition. MAKS Press, 2014, 688 pp. 3
2. Generalized model of fast ion sawtooth mixing Kadomtsev model for plasma mixing during the sawtooth crash (Fiz.Plasmy'75) was adopted in Kolesnichenko'92,'96, Gorelenkov et al.,'97,'03 for EPs. Need to generalize it for ITER conditions: non-circular cross section, arbitrary aspect ratio, finite orbit width and arbitrary helicity: Consider passing ion DF:,, 1,, 1,, 1, where 1 1 1 1 1. Need to know the energy or the magnetic moment evolution: Δ ρ sin cos, τ πτ, where 1 ω φ is the resonance factor. 4
Trapped ions are not attached to the surfaces and exchage radial locations during sawteeth: ρ, ρ, ρ δ ρ ρ φ ρ 2π. where ρ and ρ sin ω ρ ρ ρ. From here with the kernel function ρ,ρ 1 2π τ sin ρ ρ we find ρ, ρ, ρ ρ,ρ ρ φ 2π. 5
For the generalization of EP mixing as describe above we used the condition for conservation of particles density in 3D space of the constants of drift motion: The formula works for both trapped and passing particles. It takes into account the possibility of trapped particles (only) acceleration ~, / due to the large radial electric field in sawtooth [Gorelenkov et al, 97, 03]. 6
3. Formulation of the problem For D. For T: d -> t. The 3D kinetic equation for the distribution function averaged over the drift orbit has the form [1, p. 580] The first term in the r.h.s. describes Coulomb collisions, the second drift orbit averaged NES source, the last term the direct loss of ions from plasma as a result of leaving it along the orbit. Coulomb collisions of deuterium with Maxwellian deuterium, tritium, and electrons are considered. Collisions with non-maxwellian deuterium in the high-energy region and nonelastic collisions with alpha-particles are neglected because of the small density of the corresponding particles. Boundary conditions: zero fluxes at all external boundaries; known conjunction conditions for discontinuity of the averaged distribution function and continuity of the particle flux at the trapped-passing boundary (TPB). Acceptable numerical accuracy is achieved by solving for the perturbation of the Maxwellian D or T distribution. Zero initial perturbation. 7 7
The orbit-averaged source of particles emerged as a result of elastic collisions with alpha-particles [1, p. 580, 180]: 15th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems Note that the source contains only the D density; i.e., the details of the deuterium distribution function are not taken into account. This is valid because the energy of alphas is significantly higher than that of D in the thermal region, and therefore, deuterium can be considered motionless 8 before an elastic collision. 8
The reaction rate under elastic collisions of ions for some projectile-target combinations as a function of the energy of an ion incident a motionless target. The speed NES in a reference system attached to the center of mass: 15th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems The unaveraged differential scattering cross-section The source contains the distribution function of alpha-particles. This function is calculated by solving the 3D kinetic equation for alphas distribution function averaged over the drift orbits [1, par. 4.2]. The main difference from the formulation above is in the source and condition of the absence of alphas collisional flux from low energies. In these studies alphas source is calculated for Maxwellian D and T distributions, since NES rises D, T at high energies. 9 9
The model using the Maxwellian distribution function of D or T in the NESsource and in the Coulomb collision operator for alpha-particles does not allow for a number of inessential mechanisms: elastic nuclear collisions between alpha-particles and between alpha-particles and high-energy D or T, the Coulomb collisions between alpha-particles and between fast D or T. The NPA collects information on particles moving along some line-of-sight (ray) L beginning at the point where the NPA sensor is located and outputs a value proportional to the integral of the distribution function along L. Formula for the line integrated distribution (LID) is derived e.g. in [1, p. 176]: Here, E d is the energy of a particle of kind d, the multiplier a allows for the neutralisation probability and the signal attenuation along the line-ofsight L. He 4 is practically not observed on NPA due to much lower neutralization probability than D (two electrons should be captured instead of one). 10 10
ITER NPA diagnostic system High Energy Neutral Particle Analyzer HENPA Energy range: 0.1 4 MeV D/T ratio measurement at plasma core Relative position of NPA system and Neutral Beams on ITER (top view) Low Energy Neutral Particle Analyzer LENPA Energy range: 10 200 kev D/T ratio measurement at plasma edge Location: Equatorial Port 11 the sightline is perpendicular to plasma Status: leading diagnostic TUNGSTEN COLLIMATOR BEAMLINE HENPA LENPA NEUTRON DUMP 1m NEUTRON SHIELD BIOSHIELD SUPPORT STRUCTURE 11
Neutralization rate and source function of D and T knock on neutralized ions E=1MeV 20 E=1MeV Neutralisation rate, 1/s 10-2 10-3 T D Source function, x10 4 1/(m 3 *ster*ev*s) 15 10 5 D T 10-4 -1.0-0.5 0.0 0.5 1.0 Relative minor radius 0-1.0-0.5 0.0 0.5 1.0 Relative minor radius Neutralization rate for high energy ions. The ions neutralize mainly due to photorecombination and charge exchange (CX) on He + and Be 3+ The source function shows what part of plasma originates the atoms measured by NPA 12
Central sawtooth mixing. Redistribution of fusion a particles and knock on D and T ions along NPA sightline Solid - before Dashed - after Ion distribution along NPA viewline, x10 9 1/(m 3 *ev*ster) 10 He4(3.5MeV) T(1.0MeV) 1 D(1.0MeV) D, 1MeV 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 R(m) Density of ions along NPA sightline, which have the same pitch angle as NPA. Cases before/after a sawtooth event in plasma center are shown. A dip on each ion distribution is related to the shape of ion trajectories at this location (blue line) 13
Influence of sawtooth mixing on D/T ratio measurements Neutral flux, 1/(m 2 *ster*ev*s) 10 6 10 5 10 4 T integration range D integration range 0.5 1.0 1.5 2.0 E, MeV solid - before dashed - after Energy distribution of neutral flux measured by NPA before and after sawtooth event T D Arbitrary fuel ratio in % 100 99 98 97 96 95 Before After Relative change of D/T fuel ratio signal, measured by NPA NPA energy spectra respond to a sawtooth event, but the perturbation of measured D/T fuel ratio is much lower than the experimental accuracy (10%). 14
Summary Generalization of the existing Kadomtsev mixing models for the ITER case is done in the methodology of drift kinetic equations: non-circular magnetic surfaces, arbitrary aspect ratio, and significant deviations of the drift trajectories of charged fast particles from the flux surfaces. Distribution functions of He 4, D and T knock-on ions were calculated with code FPP-3D accounting for sawtooth and D, T NES on He 4. D and T neutral fluxes were calculated. It was found that the perturbation of measured D/T fuel ratio caused by sawtooth mixing is much lower than the expected experimental accuracy (10%). Thus, it can be concluded, that NPA fuel measurement is not sensitive to sawtooth mixing. 15