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    tranisition region}

Prof Róbert von Fáy-Siebenbürgen

Research Topics

Solar Physics

Studies of linear and nonlinear resonant MHD wave heating under solar atmospheric conditions.
My major new results are:

  • derivation of the generalised governing equation for resonant slow MHD waves in isotropic and anisotropic steady plasmas;
  • obtaining jump conditions to connect solutions across a resonant layer. These universal connection formulae play a crucial role, similar to the Rankine-Hugoniot relations of nonlinear gas dynamics;
  • proof of the validity of the universal character of the jump conditions in dissipative MHD and in dilute plasmas;
  • making successful applications of resonant MHD wave theory (e.g. sunspots, magnetic canopy, fibrils, coronal loops and magnetosphere);
  • developing the tools of global coronal seismology.

Studies of nano-scale reconnection MHD heating under solar atmospheric conditions.
My key new results are:

  • deriving the observational signatures of micro-scale reconnection;
  • proposing a unified model for explosive events and blinkers;
  • studying the processes of random energy deposition in magnetic flux tubes.

Space Weather/Space Plasma Physics

Studies of resonant flow instabilities in MHD involve the generalisation of stability theory when resonance occurs in a steady plasma. This theory has been extended to dilute plasmas, which more realistically describes the magnetosphere, heliosphere or space weather.
New achievements are:

  • establishing for the first time, the conditions when resonance can cause MHD flow instability far below the Kelvin-Helmholtz threshold;
  • derivation of the linear and nonlinear governing equation for dilute plasmas;
  • establishing propagation windows for linear modes.

Computational Magnetohydrodynamics (CMHD)

Modelling of explosive events (EEs), blinkers, nano-flares and solar tornadoes. EEs, blinkers and nano-flares are the smallest scale phenomena observable with the latest very high-resolution satellite techniques and are believed to be the basic building blocks of atmospheric heating. My joint ground-based (Tenerife) and satellite (SOHO, Yohkoh, TRACE) observation campaign was one out of the very few European projects supported by ESA/NASA SOHO Science Planning (11/1998).
New results are:

  • resolving the controversial 'chromospheric down-flow problem';
  • observing indirect consequences of MHD wave propagation;
  • using reconnection driven resonant MHD wave heating to derive a first unified theory combining magnetic reconnection and MHD wave heating;
  • developing a versatile software package to convert computational results into directly observable quantities taking account of non-equilibrium ionisation;
  • observing tornadoes on the Sun (this was lucky given that there is about chance in a million of success!). Gave numerous TV, radio and journal interviews on solar tornadoes.


Helioseismology provides one of the most precise measurements in astronomy and yields information about the internal structure of the Sun. Since there is a significant discrepancy between theoretical predictions and satellite measurements I am re-visiting the models of solar internal f/p/g-modes to include the combined effects of an atmospheric magnetic field, temperature and steady state changes during a solar cycle.
Novel and very exciting achievements are:

  • deriving the dispersion relation and propagation windows for magnetoacoustic-gravity surface waves in steady plasmas;
  • establishing the effect of differential rotation and meridional flow on the solar p/f-modes;
  • predicting the cyclic changes of the p/f-modes during a full solar cycle;
  • reconciliation of the results of the revisited theoretical model with observations justified my original proposal.

Stability of MHD shear flows

Stability of open shear flows is of fundamental importance in geophysics and astrophysics. Examples of such flows include plasma flows in the vicinity of the magnetopauses of the Earth and planets, the boundaries between fast and slow streams of the solar wind, the flow in the vicinity of the heliopause, flows in the interaction regions of colliding stellar winds in binary stellar systems, and astrophysical jets. To study the stability of a shear flow with respect to perturbations finite in space we have to solve an initial-value problem. Then two scenarios are possible. In the first scenario the initial finite perturbation exponentially grows at any spatial position. Such a type of instability is called absolute. In the second scenario the initial perturbation also grows exponentially, but it is swept away by the flow from any finite region so fast that it decays at any fixed spatial position. Such a type of instability is called convective. The classification of absolute and convective instability is important for the understanding of the physical processes in geophysical and astrophysical plasmas, and for the interpretation of new satellite (SOHO, TRACE, RHESSI) observational data. In spite of it fundamental importance there is little attention paid to this problem in MHD.
My novel and very exciting achievements are:

  • derived the threshold of dissipative instability of MHD tangential discontinuities which is below than the Kelvin-Helmholtz treshold;
  • the critical velocity of the dissipative instability depends on the ratio of the dissipative coeffcients at the two sides of the discontinuity and be anywhere between the negative energy wave threshold and the KHI threshold;
  • solving a classical problem of the absolute and convective instability of a tangential discontinuity in a compressible fluid;
  • establishing the effect of compressibility and dissipation on the threshold of absolute and convective instabilitity in open shear flows.

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