Paleoclassical Transport Model Description, Publications, Reports and Preprints:

          (To return to J.D. Callen homepage)

      History and physics of the paleoclassical transport model:

    The initial papers on the paleoclassical transport model were based on a key hypothesis that charged particles diffuse radially along with thin annuli of the poloidal magnetic flux in resistive, current-carrying toroidal plasmas. This key hypothesis was later shown to be the result of transforming the drift-kinetic equation from laboratory to poloidal magnetic flux coordinates, upon which Grad-Shafranov equilibria, neoclassical theory, and micro-turbulence-induced anomalous transport analyses are based.

    The diffusive components of paleoclassical transport scale with the magnetic field diffusivity induced by the electrical resistivity in the plasma, which decreases as T_e^{-3/2}. Paleoclassical radial electron heat transport can be greater than fluctuation-induced gyro-Bohm-level transport (~ T_e^{3/2}/aB^2) wherever T_e < B^{2/3} a^{1/2} keV, as usually occurs in ohmic tokamak plasmas, or wherever fluctuations are significantly reduced. Paleoclassical transport predictions have been found to compare favorably with experimental data from many ohmic-level toroidal plasmas (tokamaks, STs, RFPs, spheromaks) and in tokamak H-mode pedestals. The parameters of the paleoclassical transport model are relatively easy to evaluate.

      Initial papers on and scaling of paleoclassical radial electron heat transport:

Basic concepts in a sheared slab model:

"Most Electron Heat Transport Is Not Anomalous; It Is a Paleoclassical Process in Toroidal Plasmas," Phys. Rev. Lett. 94, 055002 (2005) (100 kB .pdf, 4 page file) -- in February 11, 2005 issue (http://prl.aps.org).

Comprehensive axisymmetric toroidal magnetic field model:

"Paleoclassical transport in low collisionality toroidal plasmas," Phys. Plasmas 12, 092512 (2005) (296 kB .pdf, 20 page file) -- in September 2005 issue (http://pop.aip.org).

Brief summary of the model and its scalings plus "back of the envelope" interpretations of various experimental results with it:

"Paleoclassical Electron Heat Transport" Oral Paper TH/1-1 at 20th IAEA Fusion Energy Conference, Vilamoura, Portugal, November 1-6, 2004, Report UW-CPTC 04-8, November 2004 (577 kB .pdf, 9 page file).

"Paleoclassical electron heat transport," Nucl. Fusion 45, 1120 (2005) -- in August 2005 issue of Nuclear Fusion (http://www.iop.org/ej/nf); expanded version of Paper TH/1-1 at 2004 IAEA Fusion Energy Conference.

      Derivation of the paleoclassical key hypothesis by transforming the drift-kinetic equation from laboratory to (locally diffusing) poloidal flux coordinates and analyzing the mathematical characteristic curves (effective particle guiding center trajectories) which oscillate about and relative to poloidal flux surfaces on the bounce time scale but diffuse radially on the slower magnetic diffusion time scale:

Original derivation based on mathematical characteristics of the drift-kinetic equation on a poloidal flux surface:

"Derivation of paleoclassical key hypothesis," Phys. Plasmas 14, 040701 (2007) (116 kB .pdf, 4 page file).

Simplified model that illustrates the physical processes underlying the paleoclassical key hypothesis:

"Response to `Comment on `Paleoclassical transport in low-collionality toroidal plasmas'' [Phys. Plasmas 14, 104701 (2007)]," Phys. Plasmas 14, 104702 (2007) (104kB .pdf, 4 page file).

Derivation starting from F = m a -- by transforming the guiding center motion equation to poloidal flux coordinates:

"Response to `Comment on `Derivation of paleoclassical key hypothesis'' [Phys. Plasmas 15, 014701 (2008)]," Phys. Plasmas 15, 104702 (2008) (108kB .pdf, 4 page file).

Discussion of how the paleoclassical transport model differs from conventional transport theory and analyses:

"Response to `Comment on `Derivation of paleoclassical key hypothesis'' [Phys. Plasmas 15, 014703 (2008)]," Phys. Plasmas 15, 104704 (2008) (80kB .pdf, 3 page file).

      Comparison of paleoclassical radial electron heat transport predictions with experimental data:

Extensive set of tests -- 18 comparisons with data from 7 different experimental devices:

"Experimental Tests Of Paleoclassical Transport," J.D. Callen, J.K. Anderson, T.C. Arlen, G. Bateman, R.V. Budny, T. Fujita, C.M. Greenfield, M. Greenwald, R.J. Groebner, D.N. Hill, G.M.D. Hogeweij, S.M. Kaye, A.H. Kritz, E.A. Lazarus, A.C. Leonard, M.A. Mahdavi, H.S. McLean, T.H. Osborne, A.Y. Pankin, C.C. Petty, J.S. Sarff, H.E. St. John, W.M. Stacey, D. Stutman, E.J. Synakowski, and K. Tritz, Paper EX/P3-2 at 21st IAEA Fusion Energy Conference, Chengdu, China, October 16-21, 2006, Report UW-CPTC 06-5, October 2006 (4.5 MB .pdf, 8 page file).

"Experimental tests of paleoclassical transport," J.D. Callen, J.K. Anderson, T.C. Arlen, G. Bateman, R.V. Budny, T. Fujita, C.M. Greenfield, M. Greenwald, R.J. Groebner, D.N. Hill, G.M.D. Hogeweij, S.M. Kaye, A.H. Kritz, E.A. Lazarus, A.C. Leonard, M.A. Mahdavi, H.S. McLean, T.H. Osborne, A.Y. Pankin, C.C. Petty, J.S. Sarff, H.E. St. John, W.M. Stacey, D. Stutman, E.J. Synakowski, and K. Tritz, Nucl. Fusion 47, 1449 (2007) -- in November 2007 issue of Nuclear Fusion (http://www.iop.org/ej/nf); expanded version of Paper EX/P3-2 at 2006 IAEA Fusion Energy Conference.

Paleoclassical prediction of linear ohmic confinement regime, ECH "stair-step" response in RTP and electron Internal Transport Barriers around q=1 surface in TEXTOR:

"Paleoclassical transport explains electron transport barriers in RTP and TEXTOR," G.M.D. Hogeweij, J.D. Callen, the RTP Team and the TEXTOR Team, Plasma Phys. Control. Fusion 50, 065011 (2008) (http://www.iop.org/ej/ppcf).

Transport modeling of the T_e profiles in DIII-D H-modes which found "The paleoclassical transport model together with the ETG component of the GLF23 model are found to be needed in order to produce the observed edge pedestal in these DIII-D simulations:"

"Simulation of electron thermal transport in H-mode discharges," T. Rafiq, A.Y. Pankin, G. Bateman, A.H. Kritz, and F.D. Halpern, Phys. Plasmas 16, 032505 (2009) (http://pop.aip.org).

      Evaluating the parameters of the paleoclassical transport model is straightforward:

"Cookbook" for evaluating paleoclassical transport model parameters:

"Paleoclassical Electron Heat Transport Model," Report UW-CPTC 07-5, December 2007 (252 kB .pdf, 14 page file).