| Title:
|
A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations (English) |
| Author:
|
Núñez, Manuel |
| Author:
|
Rojo, Jesús |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
23-38 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Small perturbations of an equilibrium plasma satisfy the linearized magnetohydrodynamics equations. These form a mixed elliptic-hyperbolic system that in a straight-field geometry and for a fixed time frequency may be reduced to a single scalar equation div$\left(A_1\Delta_u\right) + A_2u =0$, where $A_1$ may have singularities in the domaind $U$ of definition. We study the case when $U$ is a half-plane and $u$ possesses high Fourier components, analyzing the changes brought about by the singularity $A_1 = \infty$. We show that absorptions of energy takes place precisely at this singularity, that the solutions have a near harmonic character, and the integrability characteristics of the boundary data are kept throughout $U$. (English) |
| Keyword:
|
magnetohydrodynamics |
| Keyword:
|
Alfvén waves |
| Keyword:
|
Fourier analysis |
| Keyword:
|
singularity |
| Keyword:
|
small perturbations |
| Keyword:
|
equilibrium plasma |
| Keyword:
|
mixed elliptic-hyperbolic system |
| MSC:
|
34E05 |
| MSC:
|
34E20 |
| MSC:
|
35Q35 |
| MSC:
|
35Q60 |
| MSC:
|
76W05 |
| idZBL:
|
Zbl 0778.76100 |
| idMR:
|
MR1202078 |
| DOI:
|
10.21136/AM.1993.104532 |
| . |
| Date available:
|
2008-05-20T18:44:52Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104532 |
| . |
| Reference:
|
[1] Grad H.: .Phys. Today 22 (1969), 34. Zbl 0181.28501 |
| Reference:
|
[2] Chen L., Hasegawa A.: Plasma heating by spatial resonance of Alfvén wave.Phys. of Fluids 17(1974), 1399-1403. 10.1063/1.1694904 |
| Reference:
|
[3] Tataronis J., Talmadge J. N., Shohet J. L.: Alfvén wave heating in general toroidal geometry.Univ. of Wisconsin Report (1978). |
| Reference:
|
[4] Chen L., Hasegawa A.: Steady State excitation of field line resonance.J. of Geoph. Res. 79 (1974), 1024-1037. 10.1029/JA079i007p01024 |
| Reference:
|
[5] Kivelson M. G., Southwood D. J.: Resonant ULF waves: A new interpretation.Geoph. Res. Letters 12 (1985), 49-52. 10.1029/GL012i001p00049 |
| Reference:
|
[6] Freidberg J. P.: Ideal Magnetohydrodynamic theory of magnetic fusion systems.Rev. of Modern Phys. 54 (1982), 801-902. 10.1103/RevModPhys.54.801 |
| Reference:
|
[7] Tataronis J. A.: Energy absorption in the continuous spectrum of ideal Magnetohydrodynamics.J. Plasma Phys. 13 (1975), 87-105. 10.1017/S0022377800025897 |
| Reference:
|
[8] Sedlacek Z.: Electrostatic oscillations in cold inhomogeneous plasma.J. Plasma Phys. 5 (1971), 239-263. 10.1017/S0022377800005754 |
| Reference:
|
[9] Grossmann W.,Tataronis J. A.: Decay of MHD waves by phase mixing II: the Theta-Pinch in cylindrical geometry.Z. Physik 261 (1973), 217-236. 10.1007/BF01391914 |
| Reference:
|
[10] Bender C. M., Orszag S. A.: Advanced Mathematical Methods for Scientist and Engineers.McGraw-Hill, 1984. MR 0538168 |
| Reference:
|
[11] Olver F. W. J.: Asymptotics and Special Functions.Academic Press, 1974. Zbl 0308.41023, MR 0435697 |
| Reference:
|
[12] Stein E. M., Weiss G.: Introduction to Fourier Analysis on Euclidean Spaces.Princeton University Press, 1975. MR 0304972 |
| . |
