# On Ponderomotive Effects Induced by Alfvén Waves in Inhomogeneous 2.5D MHD Plasmas

- 242 Downloads
- 11 Citations

## Abstract

Where spatial gradients in the amplitude of an Alfvén wave are non-zero, a nonlinear magnetic-pressure gradient acts upon the medium (commonly referred to as the *ponderomotive force*). We investigate the nature of such a force in inhomogeneous 2.5D MHD plasmas by analysing source terms in the nonlinear wave equations for the general case of inhomogeneous **B** and *ρ*, and consider supporting nonlinear numerical simulations. Our equations indicate that there are two distinct classes of ponderomotive effect induced by Alfvén waves in general 2.5D MHD, each with *both* a longitudinal and transverse manifestation. i) Geometric effects: Gradients in the pulse geometry relative to the background magnetic field cause the wave to sustain cospatial disturbances, the *longitudinal* and *transverse daughter disturbances* – where we report on the transverse disturbance for the first time. ii) ∇(*c* _{A}) effects: Where a pulse propagates through an inhomogeneous region (where the gradients in the Alfvén-speed profile *c* _{A} are non-zero), the nonlinear magnetic-pressure gradient acts to accelerate the plasma. Transverse gradients (phase mixing regions) excite independently propagating fast magnetoacoustic waves (generalising the result of Nakariakov, Roberts, and Murawski (*Solar Phys.* **175**, 93, 1997)) and longitudinal gradients (longitudinally dispersive regions) perturb along the field (thus creating static disturbances in *β*=0, and slow waves in *β*≠0). We additionally demonstrate that mode conversion due the nonlinear Lorentz force is a one-way process, and does not act as a mechanism to nonlinearly generate Alfvén waves due to propagating magnetoacoustic waves. We conclude that these ponderomotive effects are induced by an Alfvén wave propagating in any MHD medium, and have the potential to have significant consequences on the dynamics of energy transport and aspects of dissipation provided the system is sufficiently nonlinear and inhomogeneous.

## Keywords

Magnetic fields, corona Waves, Alfvén Waves, magnetohydrodynamic Waves, propagation## Notes

### Acknowledgements

The authors acknowledge IDL support provided by STFC. JOT acknowledges travel support provided by the RAS and the IMA, and a Ph.D. scholarship provided by Northumbria University. The computational work for this paper was carried out on the joint STFC and SFC (SRIF) funded cluster at the University of St Andrews (Scotland, UK).

## References

- Allan, W., Poulter, E.M., Manuel, J.R.: 1991,
*J. Geophys. Res.***96**, 11461 – 11473. ADSCrossRefGoogle Scholar - Arber, T.D., Longbottom, A.W., Gerrard, C.L., Milne, A.M.: 2001,
*J. Comput. Phys.***171**, 151 – 181. MathSciNetADSCrossRefzbMATHGoogle Scholar - Botha, G.J.J., Arber, T.D., Nakariakov, V.M., Keenan, F.P.: 2000,
*Astron. Astrophys.***363**, 1186 – 1194. ADSGoogle Scholar - Boyd, T.J.M., Sanderson, J.J.: 2003,
*The Physics of Plasmas*, Cambridge University Press, Cambridge, 40 – 47. CrossRefzbMATHGoogle Scholar - Champeaux, S., Passot, T., Sulem, P.L.: 1997,
*J. Plasma Phys.***58**, 665 – 690. ADSCrossRefGoogle Scholar - Chen, F.F.: 1984,
*Introduction to Plasma Physics and Controlled Fusion*, Springer, Berlin, 55 – 89. CrossRefGoogle Scholar - De Moortel, I., Nakariakov, V.M.: 2012,
*Phil. Trans. Roy. Soc. London***370**, 3193 – 3216. ADSCrossRefGoogle Scholar - Falle, S.A.E.G., Hartquist, T.W.: 2002,
*Mon. Not. Roy. Astron. Soc.***329**, 195 – 203. ADSCrossRefGoogle Scholar - Goossens, M., Erdélyi, R., Ruderman, M.S.: 2011,
*Space Sci. Rev.***158**, 289 – 338. ADSCrossRefGoogle Scholar - Grimshaw, R., Pelinovsky, D., Pelinovsky, E.: 2010,
*Wave Motion***99**, 496 – 507. MathSciNetCrossRefGoogle Scholar - McLaughlin, J.A., De Moortel, I., Hood, A.W.: 2011,
*Astron. Astrophys.***527**, A149. ADSCrossRefGoogle Scholar - Nakariakov, V.M., Roberts, B., Murawski, K.: 1997,
*Solar Phys.***175**, 93 – 105. ADSCrossRefGoogle Scholar - Nakariakov, V.M., Verwichte, E.O.: 2005,
*Living Rev. Solar Phys.***2**(3). http://solarphysics.livingreviews.org/Articles/lrsp-2005-3. - Rankin, R., Frycz, P., Tikhonchuk, V.T., Samson, J.C.: 1994,
*J. Geophys. Res.***99**, 21291 – 21302. ADSCrossRefGoogle Scholar - Stark, B.A., Musielak, Z.E., Suess, S.T.: 1995, In: Winterhalter, D., Gosling, J.T., Habbal, S.R., Kurth, W.S., Neugebauer, M. (eds.)
*Solar Wind Eight*,*AIP Conf. Proc.***382**, 153 – 156. Google Scholar - Tikhonchuk, V.T., Rankin, R., Frycz, P., Samson, J.C.: 1995,
*Phys. Plasmas***2**, 501 – 515. ADSCrossRefGoogle Scholar - Ulmschneider, P., Narain, U.: 1990, In: Priest, E.R., Krishan, V. (eds.)
*Basic Plasma Processes on the Sun*,*IAU Symp.***142**, 97. CrossRefGoogle Scholar - Verwichte, E.: 1999, “Aspects of Nonlinearity and Dissipation in Magnetohydrodynamics”, Ph.D. thesis, The Open University. Google Scholar
- Verwichte, E., Nakariakov, V.M., Longbottom, A.W.: 1999,
*J. Plasma Phys.***62**, 219 – 232. ADSCrossRefGoogle Scholar - Webb, G.M., Zakharian, A.R., Brio, M., Zank, G.P.: 2001,
*J. Plasma Phys.***66**, 167 – 212. ADSCrossRefGoogle Scholar - Webb, G.M., Zank, G.P., Kaghashvili, E.K., Ratkiewicz, R.E.: 2005,
*J. Plasma Phys.***71**, 811 – 857. ADSCrossRefGoogle Scholar