One can read several key papers on NOVA codes which are often used for studying the stability properties of TAE modes. The trapped electron collisional damping is implemented according to Ref.[#3]. Drift kinetic formulation including finite orbit width (FOW) effects can be found in Ref. [#4]. In that reference an important result was confirmed numerically that FOW lead to a plateau in the growth rate dependence on the toroidal mode number which limits the number of unstable modes in ITER for example.

The NOVA codes are widely used to study the linear stability properties of Alfvénic modes and were extensively verified and validated, [#5].

General information on how to run NOVA/NOVA-K (up to version 2, i.e. up to 2014ish) can be found on PPPL theory linux cluster at /u/ngorelen/SRC/Equil/Readme for NOVA (including qsolver equilibrium) and at /u/ngorelen/SRC/NOVAK/Readme-K. It is available to be used for many US fusion researchers.

Future plans.

An extensive upgrade of this suite (version 3) is going on. It includes

[1] C. Z. Cheng, M. C. Chang, Phys. Fluids

[2] C. Z. Cheng, Phys. Reports

[3] G. Y. Fu, C. Z. Cheng, K. L. Wong, Phys. Fluids B

[4] N. N. Gorelenkov, C. Z. Cheng, G. Y. Fu, Phys. Plasmas

[5] M. A. Van Zeeland, G. J. Kramer, M. E. Austine et al., Phys. Rev. Lett.

Other resources on VV are page.

1) formulation and examples of its simulations:

ideal MHD part:

@article{ChengPF86, AUTHOR = "C. Z. Cheng and M. S. Chance",

TITLE = "Low-n shear \protect{Alfv\'{e}}n spectra in axisymmetric toroidal plasmas",

JOURNAL = "Phys. Fluids",

VOLUME = "29",

PAGES = "3695--3701",

MONTH = "November",

YEAR = "1986"}

@article{ChengPhR92,

AUTHOR = "C. Z. Cheng",

TITLE = "Kinetic extensions of magnetohydrodynamics for axisymmetric toroidal plasmas",

JOURNAL = "Phys. Reports",

VOLUME = "211",

PAGES = "1--51",

MONTH = "January",

YEAR = "1992"}

New kinetic effects are added (NOVA-K), such as trapped electron collisoinal damping (orbit width effects shown in this paper are not used any more):

G. Y. Fu and C. Z. Cheng and K. L. Wong, "Stability of the

toroidicity-induced \protect{A}lfv\'{e}n eigenmode in axisymmetric

toroidal equilibria", Phys. Fluids B, V.5, pp.4040--4050 (1993);

this paper give a description of the radiative damping implementation in NOVA

"Analysis of alpha particle-driven toroidal Alfven eigenmodes in TFTR deuterium-tritium experiments"

G.-Y. Fu, C.Z. Cheng, et.al. Phys.Plasmas, v.3. 4036-4045 (1996).

this paper has accurate orbit width effect described, which are used in NOVA

N. N. Gorelenkov and C. Z. Cheng and G. Y. Fu, "Fast particle finite

orbit width and Larmor radius effects on low-n toroidicity induced

\protect{A}lfv\'{e}n eigenmode excitation", Phys. Plasmas, v.6,

pp. 2802-2807 (1999). }

here we describe the model for the distribution function of beam ions used in NOVA under the option "l"

@article{GorelenkovNF05ITER,

AUTHOR = "N. N. Gorelenkov and H. L. Berk and R. V. Budny",

TITLE = "Beam anisotropy effect on \protect{Alfv\'{e}}n eigenmode stability in ITER-like plasmas",

JOURNAL = "Nucl. Fusion",

VOLUME = "45",

PAGES = "226--237",

MONTH = "March",

YEAR = "2005"}

2) TAE and RSAE radial structures are verified (arguably the best MHD code/experiment comparison).

@article{VanzeelandPRL06,

AUTHOR = "M. A. Van Zeeland and G. J. Kramer and M. E. Austin and R. L. Boivin and W. W. Heidbrin and M. A. Makowski and G. R. McKee and R. Nazikian and W. M. Solomon and G. Wang",

TITLE = "Radial Structure of \protect{Alfv\'{e}}n Eigenmodes in the DIII-D Tokamak through Electron-Cyclotron-Emission Measurements",

JOURNAL = "Phys. Rev. Letters",

VOLUME = "97",

PAGES = "135001-1--135001-4",

MONTH = "September",

YEAR = "2006"}

3) Simulations of TAE observations in TFTR advanced after more theoretical insight was available.

@article{NazikianPRL03,

AUTHOR = "R. Nazikian and G. J. Kramer and C. Z. Cheng and N. N. Gorelenkov and H. L. Berk and S. E. Sharapov",

TITLE = "New Interpretation of Alpha-Particle-Driven Instabilities in Deuterium-Tritium Experiments on the Tokamak Fusion Test Reactor",

JOURNAL = "Phys. Rev. Lett.",

VOLUME = "91",

PAGES = "125003-1--125003-4",

MONTH = "September",

YEAR = "2003"}

4) Stability calculations in NSTX for low frequency TAEs and comparisons with high frequency mode observations.

@article{GorelenkovPoP04,

AUTHOR = "N. N. Gorelenkov and E. Belova and H. L. Berk and C. Z. Cheng and E. D. Fredrickson and W. W. Heidbrink and S. Kaye and G. J. Kramer",

TITLE = "Beam ion driven instabilities in National Spherical Tokamak Experiment",

JOURNAL = "Phys. Plasmas",

VOLUME = "11",

PAGES = "2586--2596",

MONTH = "May",

YEAR = "2004"}

5) Another nice application of NOVA for RSAEs in DIII-D and JET.

@article{KramerPoP2006,

AUTHOR = "G. J. Kramer and R. Nazikian and B. Alper and M. de Baar and et. al.",

TITLE = "Interpretation of core localized \protect{Alfv\'{e}}n eigenmodes in DIII-D and Joing European Torus reversed magnetic shear plasmas",

JOURNAL = "Phys. Plasmas",

VOLUME = "13",

PAGES = "056104-1--056104-7",

MONTH = "May",

YEAR = "2006"}

6) Projections to ITER.

@article{GorelenkovNF03BP,

AUTHOR = "N. N. Gorelenkov and H. L. Berk and R. V. Budny and C. Z. Cheng and G. Y. Fu and W. W. Heidbrink and G. J. Kramer and D. Meade and R. Nazikian",

TITLE = "Study of thermonuclear \protect{Alfv\'{e}}n instabilities in next step burning plasma proposals",

JOURNAL = "Nucl. Fusion",

VOLUME = "43",

PAGES = "594--605",

MONTH = "July",

YEAR = "2003"}

@article{GorelenkovNF05ITER,

AUTHOR = "N. N. Gorelenkov and H. L. Berk and R. V. Budny",

TITLE = "Beam anisotropy effect on \protect{Alfv\'{e}}n eigenmode stability in ITER-like plasmas",

JOURNAL = "Nucl. Fusion",

VOLUME = "45",

PAGES = "226--237",

MONTH = "March",

YEAR = "2005"}