Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak
The linear response of a plasma to perturbations of arbitrary frequency and wavelength is derived for any axisymmetric magnetized toroidal plasma. An explicit transformation to action-angle coordinates is achieved using orthogonal magnetic coordinates and the Littlejohn Lagrangian, establishing the...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-03-01
|
| Series: | Fundamental Plasma Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2772828525000019 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850228593090625536 |
|---|---|
| author | M. Fitzgerald B.N. Breizman |
| author_facet | M. Fitzgerald B.N. Breizman |
| author_sort | M. Fitzgerald |
| collection | DOAJ |
| description | The linear response of a plasma to perturbations of arbitrary frequency and wavelength is derived for any axisymmetric magnetized toroidal plasma. An explicit transformation to action-angle coordinates is achieved using orthogonal magnetic coordinates and the Littlejohn Lagrangian, establishing the validity of this result to arbitrary order in normalized Larmor radius. The global resonance condition for compressional modes is clarified in more detail than in previous works, confirming that the poloidal orbit-average of the cyclotron frequency gives the desired result at lowest order in Larmor radius. The global plasma response to the perturbation at each resonance is captured by a poloidal and gyroaverage of the perturbing potential. A “global gyroaveraging” of the potential is a natural by-product of this analysis which takes into account the changing of the magnetic field over an orbit. The resonance condition depends on two arbitrary integers which completely separately capture the effects poloidal non-uniformity and finite Larmor radius in generating sidebands. We learn that poloidal sidebands generated for compressional modes are dominated by the change in gyrofrequency over the orbit, which is very different to shear modes where the gyrofrequency only contributes via a finite Larmor radius effect. This increases the number of bounce harmonics required to compute the linear drive, giving a more complicated resonance map. An example calculation is given comparing resonance of shear and compressional modes in a published DIII-D case. |
| format | Article |
| id | doaj-art-eabf1b4211fc4073913fd0adf4e41acb |
| institution | OA Journals |
| issn | 2772-8285 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Fundamental Plasma Physics |
| spelling | doaj-art-eabf1b4211fc4073913fd0adf4e41acb2025-08-20T02:04:28ZengElsevierFundamental Plasma Physics2772-82852025-03-011310008410.1016/j.fpp.2025.100084Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamakM. Fitzgerald0B.N. Breizman1United Kingdom Atomic Energy Authority, Culham Campus, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK; Corresponding author.Institute for Fusion Studies, The University of Texas, Austin, TX 78712, USAThe linear response of a plasma to perturbations of arbitrary frequency and wavelength is derived for any axisymmetric magnetized toroidal plasma. An explicit transformation to action-angle coordinates is achieved using orthogonal magnetic coordinates and the Littlejohn Lagrangian, establishing the validity of this result to arbitrary order in normalized Larmor radius. The global resonance condition for compressional modes is clarified in more detail than in previous works, confirming that the poloidal orbit-average of the cyclotron frequency gives the desired result at lowest order in Larmor radius. The global plasma response to the perturbation at each resonance is captured by a poloidal and gyroaverage of the perturbing potential. A “global gyroaveraging” of the potential is a natural by-product of this analysis which takes into account the changing of the magnetic field over an orbit. The resonance condition depends on two arbitrary integers which completely separately capture the effects poloidal non-uniformity and finite Larmor radius in generating sidebands. We learn that poloidal sidebands generated for compressional modes are dominated by the change in gyrofrequency over the orbit, which is very different to shear modes where the gyrofrequency only contributes via a finite Larmor radius effect. This increases the number of bounce harmonics required to compute the linear drive, giving a more complicated resonance map. An example calculation is given comparing resonance of shear and compressional modes in a published DIII-D case.http://www.sciencedirect.com/science/article/pii/S2772828525000019VlasovEnergetic particlesLinear kineticResonanceTokamakCompressional |
| spellingShingle | M. Fitzgerald B.N. Breizman Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak Fundamental Plasma Physics Vlasov Energetic particles Linear kinetic Resonance Tokamak Compressional |
| title | Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak |
| title_full | Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak |
| title_fullStr | Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak |
| title_full_unstemmed | Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak |
| title_short | Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak |
| title_sort | solution of the linear wave particle kinetic equation for global modes of arbitrary frequency in a tokamak |
| topic | Vlasov Energetic particles Linear kinetic Resonance Tokamak Compressional |
| url | http://www.sciencedirect.com/science/article/pii/S2772828525000019 |
| work_keys_str_mv | AT mfitzgerald solutionofthelinearwaveparticlekineticequationforglobalmodesofarbitraryfrequencyinatokamak AT bnbreizman solutionofthelinearwaveparticlekineticequationforglobalmodesofarbitraryfrequencyinatokamak |