Differential formulation of the gyrokinetic Landau operator
Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the socalled Landau representation, this work investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Finally, based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.
 Authors:

^{[1]}
;
^{[2]};
^{[1]}
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Saint Michael's College, Colchester, VT (United States). Dept. of Physics
 Publication Date:
 Report Number(s):
 PPPL5340
Journal ID: ISSN 00223778; PII: S0022377816001203
 Grant/Contract Number:
 AC0209CH11466; SC0014032
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Plasma Physics
 Additional Journal Information:
 Journal Volume: 83; Journal Issue: 1; Journal ID: ISSN 00223778
 Publisher:
 Cambridge University Press
 Research Org:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Saint Michael's College, Colchester, VT (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC24)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; fusion plasma; plasma nonlinear phenomena; plasma simulation
 OSTI Identifier:
 1351535
Hirvijoki, Eero, Brizard, Alain J., and Pfefferlé, David. Differential formulation of the gyrokinetic Landau operator. United States: N. p.,
Web. doi:10.1017/s0022377816001203.
Hirvijoki, Eero, Brizard, Alain J., & Pfefferlé, David. Differential formulation of the gyrokinetic Landau operator. United States. doi:10.1017/s0022377816001203.
Hirvijoki, Eero, Brizard, Alain J., and Pfefferlé, David. 2017.
"Differential formulation of the gyrokinetic Landau operator". United States.
doi:10.1017/s0022377816001203. https://www.osti.gov/servlets/purl/1351535.
@article{osti_1351535,
title = {Differential formulation of the gyrokinetic Landau operator},
author = {Hirvijoki, Eero and Brizard, Alain J. and Pfefferlé, David},
abstractNote = {Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the socalled Landau representation, this work investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Finally, based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.},
doi = {10.1017/s0022377816001203},
journal = {Journal of Plasma Physics},
number = 1,
volume = 83,
place = {United States},
year = {2017},
month = {1}
}