Status of the CQL3D-FOW Project

Yu.V. Petov (petrov@compxco.com) and R.W. Harvey (CompX)

DOE Workshop in Integrated Simulations for MFE Sciences, May 18-19, 2015.

Panel C. Oral Presentation Requested

Introduction: The continuum bounce-averaged, toroidally symmetric FP code CQL3D [1] forf e , i (u0,θ0,ρ0 ;t ) , developed by CompX, is used by many national laboratories, universities and

private companies inside and outside the U.S. f e ,i (u0,θ0,ρ0) are midplane distributions as a function of midplane relativisitic velocity, pitch angle, and flux label, respectively; off-midplane f(R,Z) is obtained in accord with the constants of motion. The code is favored by experimentalists because of (1) physics-based modeling of RF/NBI induced nonthermal distribution functions, (2) its large set of synthetic diagnostics tools, (3) speed, (4) simplicity of use starting from a set of run templates, and (5) ready support from CompX. RF fields are obtained from the general frequency GENRAY[2] ray tracing code, or full wave codes AORSA[3] and TORIC[4,5]. Quasilinear (QL) theory, or a first principles calculation with the Lorentz gyro-orbit code DC [6], is used in obtaining the RF diffusion. The internal NFREYA NBI fast ion source is benchmarked against NUBEAM[7]. CQL3D is also coupled to other software such as the Plasma State, and is part of the SciDAC Integrated Plasma Simulator project, and is presently being integrated into TRANSP[8]. A fast reduced model is achieved by averaging the kinetic equations over all periodic coordinates under the assumption of low collisionality, which is typically valid for the nonthermal particles in the core.

CQL3D work from 1985 to 2010 employed a zero-orbit-width (ZOW) approximation for particle bounce-motion, neglecting off-flux-surface drifts. This is usually valid for electrons, and has been applied to RF current drive and runaway electron calculations. However, ZOW is often not sufficiently accurate for ion velocity distributions. Since 2010, the focus has been more on the effects of inclusion of a finite-orbit-width (FOW) guiding-center model for ion motion, particularly in NSTX.

Methods: The FP equation in terms of the midplane coordinates I = (u0, θ0, R0) (as COM) is ∂∂ t

J f 0(I , t ) = ∂∂ I i

J [Dij ∂∂ I j

−F i ] f 0( I , t ) + J ⟨S ⟩

with Jacobian J. The bounce-averaged diffusion coefficients resulting from the local collisional or QLRF diffusion are given by Dij=⟨(∂ I i / ∂u)Du u(∂ I j /∂ u) ⟩ , and the drag is given by

F i= ⟨(∂ I i / ∂u)⋅Fu ⟩ , where the tensor Duu and vector Fu are the local collisional plus QL RF

diffusion coefficients and the collisional friction, respectively. The last term is the bounce-average NBI source term. The Coulomb collisions and RF QL diffusion are a spatially local phenomena,

changing only a particles velocity u, not position, but their combination with transformation coefficients ∂ I /∂utogether with bounce averaging results inappearance of neoclassical radial transport terms. Solution is finite-volume, time-implicit.

Results: Past ZOW work has focused on electron modeling, including ECCD [9,10] on DIII-D (Fig. 1) and LHCD on C-Mod [11,12]. Validation against experiment was done by comparison withcurrent profiles, and synthetic diagnosticsfor hard Xray spectra and electron cyclotron emission.

<= Suggests radial transport spreading

Fig. 1.

Validation of full-FOW CQL3D [13,14] has included comparison with standard bootstrap current models [15]. Fig. 2a is for NSTX at 4X actual B-fields, showing iteration to agreement. The FOW affects are accentuated in the actual lower B-fields (Fig. 2b).

The FOW experimental validation has focused on modeling a time-dependent NBI and NBI+HHFW shot on NSTX, using the faster CQL3D-Hybrid-FOW. Fig. 3a-d shows agreement of FIDA and neutron synthetic diagnostics with experiment. NPA spectra also agreed well [16].

Continuing work: In addition to finishing details for the full FOW code, the support and maintenance of both ZOW and FOW versions of CQL3D is planned. This will involve validations for the code against past theory and experimental plasmas. Applications will be made in interpretation of present fusion experiments, and to extrapolations to ITER. The code suite will be further coupled withwhole plasma models.

ρ=0.1

Fig. 3. The FIDA experiment consists of 10 NBI pulses (a) and additional steady HHFW (b). FIDA is averaged over the last 4 beam pulses. (c) and (d) give respective neutron rates, as validation of the code calculation of the elevated fast ion levels, heating rates, and collisional slowing down rates.

(a)

(b)

(c)

(d)

Raxis

Fig. 2. Bootstrap current profiles: Black curves are from Hirshman/Sauter model, green curves converging to red curve – from full-FOW calculations (40 time steps, 0-2 sec of physical time).

(a) (b)

References:

[1] R.W. Harvey and M.G. McCoy, The CQL3D Fokker-Planck Code, Proc. of IAEA Technical Committee Meeting on Advances in Simulation and Modeling of Thermonuclear Plasmas, Montreal, 1992, p. 489-526, IAEA, Vienna (1993); www . compxco . com / cql 3 d . html ; Google CQL3D CompX.

[2] A.P. Smirnov and R.W. Harvey, The GENRAY Ray Tracing Code, CompX report CompX-2000-01 (2001); .http://www.compxco.com/genray.html

[3] Jaeger, E.F., Berry, L.A., D'Azevedo, E., Batchelor, D.B., Carter, M.D., White, K.F., and Weitzner, H., “Advances in full-wave modeling of radio frequency heated, multidimensional plasmas,” Phys. Plasmas 9, 1873 (2002); E. F. Jaeger, R. W. Harvey, L. A. Berry, et al., “Self-Consistent Full-Wave and Fokker-Planck Calculations for Ion Cyclotron Heating in Non-Maxwellian Plasmas”, Phys. of Plasmas 13, 056101 (2006).

[4] M. Brambilla, “Numerical simulation of ion cyclotron waves in tokamak plasmas”, Plasma Phys. Controlled Fusion 41, 1 (1999).

[5] J. C. Wright, P. T. Bonoli, and A. E. Schmidt, M. A. Brambilla, C. K. Phillips and E. J. Valeo R.W. Harvey, “An assessment of full-wave effects on the propagation and absorption of lowerhybrid waves'', APS invited talk, to be published in Phys. of Plasmas (2009)

[6] Harvey, R.W., Petrov, Yu., Jaeger, E.F., Berry, L.A., Batchelor, D. B., Bonoli, P.T., and Wright, J.C., “Comparison of ICRF-Induced Ion Diffusion Coefficients Calculated with the DC and AORSA Codes,” Proc. of 18th Topical Conference on. Radio Frequency Power in Plasmas, Ghent, (2009).

[7] A. Pankin, D. McCune, R. Andre et al., "The Tokamak Monte Carlo Fast Ion Module NUBEAM in the National Transport Code Collaboration Library",Computer Physics Communications Vol. 159,No. 3 (2004) 157-184.

[8] R.J. Hawryluk, "An Empirical Approach to Tokamak Transport", in Physics of Plasmas Close to Thermonuclear Conditions, ed. by B. Coppi, et al., (CEC, Brussels, 1980), Vol. 1, pp. 19-46; J. Ongena, M. Evrard, D. McCune, "Numerical Transport Codes", in the Proceedings of the Third Carolus Magnus Summer School on Plasma Physics, (Spa, Belgium, Sept 1997), as published in Transactions of Fusion Technology, March, 1998, Vol. 33, No. 2T, pp. 181-191.

[9] T.C. Luce, Y.R. Lin-Liu, J.M. Lohr, C.C. Petty, R. Prater, G. Giruzzi, R.W. Harvey, and B.W. Rice,``Generation of Localized Non-Inductive Current by Electron Cyclotron Waves on the DIII-D Tokamak'', Phys. Rev. Lett. 83, 4550 (1999).

[10] C.C.Petty et al., "Electron Cyclotron Wave Experiments on DIII-D", 14th Topical Conference on Radiofrequency Power in Plasmas, Oxnard, in AIP Conf. Proc. (2001).

[11] A.E. Schmidt, P.T. Bonoli, A.E. Hubbard et al, “Measurements and Modeling of X-Ray and ECE Spectra During C-Mod LHCD Experiments”, Proc. of 17th Top. Conf. on RF Power in Plasmas, Eds. P.M. Ryan, D.A. Rasmussen, AIP Conf. Proc 933, p. 281 (2007).

[12] G. M. Wallace, R. R. Parker, P. T. Bonoli, A. E. Hubbard, J. W. Hughes, B. L. LaBombard, O. Meneghini, A. E. Schmidt, S. Shiraiwa, D. G. Whyte, J. C. Wright, S. J. Wukitch, R. W. Harvey, A. P. Smirnov, and J. R. Wilson, “Absorption of lower hybrid waves in the scrape off layer of a divertedtokamak”, Physics of Plasmas, 17, 082508 (2010).

[13] Yu.V. Petrov and R.W. Harvey, “Finite Orbit Width Features in the CQL3D Code”, 24th IAEA Fusion Energy Conference, San Diego, 2012, TH/P6-02.

[14] Yu.V. Petrov and R.W. Harvey, “Finite-Orbit-Width Version of the CQL3D for Description of RF-Enhanced Neoclassical Transport”, to be published in Proc. of 21st Topical Conf. on Radiofre-quency Power in Plasmas, Arrowhead, in AIP Conf. Proc. (2015).

[15] O. Sauter, C. Angioni, and Y. R. Lin-Liu, “Neoclassical conductivity and bootstrap current for-mulas for general axisymmetric equilibria and arbitrary collisionality regime”, Phys. Plasmas 6 (1999) 2834. Also: S.P. Hirshman, “Finite-aspect-ratio effects on the bootstrap current in tokamaks”,Phys. Fluids 31, 3150 (1988).

[16] R.W. Harvey, Yu.V. Petrov, D. Liu, W.W. Heidbrink, G. Taylor, P.T. Bonoli, “NBI and HHFWFast Ion Temporal Dynamics Modeling with CQL3D-Hybrid-FOW in NSTX Discharges”, 25thIAEA Fusion Energy Conference, St. Petersburg, Russia, (2014), TH/P6-49.