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Nikolay Petrukhin

  • Tenured Professor (2005)
  • Distinguished Professor (2018)
  • Nikolay Petrukhin has been at HSE University since 2003.

Education, Degrees and Academic Titles

  • 1985
  • 1984

    Doctor of Sciences* in Astrophysics Stellar and Astronomy
    Leningrad State University

  • 1962

    Gorky Ural State University

* Doctor of Sciences
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.

Courses (2019/2020)

Courses (2018/2019)

Linear Algebra (Bachelor’s programme; Faculty of Economics; 1 year, 2, 3 module)Rus

Courses (2017/2018)

Linear Algebra (Bachelor’s programme; Faculty of Economics; 1 year, 1, 2 module)Rus

Courses (2016/2017)

Linear Algebra (Bachelor’s programme; Faculty of Economics; 1 year, 1, 2 module)Rus


Phase mixing of Alfvén waves propagating in non-reflective magnetic plasma configurations

The ability of phase mixing to provide efficient damping of Alfvén waves even in weakly dissipative plasmas made it a popular mechanismforexplainingthesolarcoronalheating.Initiallyitwasstudiedintheequilibriumconfigurationswiththestraightmagnetic fieldlinesandtheAlfvénspeedonlyvaryinginthedirectionperpendiculartothemagneticfield.LatertheanalysisoftheAlfvénwave phase mixing was extended in various directions. In particular it was studied in two-dimensional planar magnetic plasma equilibria. Analytical investigation was carried out under the assumption that the wavelength is much smaller than the characteristic scale of the background quantity variation. This assumption enabled using the Wentzel, Kramers, and Brillouin (WKB) method. When it is not satisfied the study was only carried out numerically. In general, even the wave propagation in a one-dimensional inhomogeneous equilibrium can be only studied numerically. However there is one important exception, so-called non-reflective equilibria. In these equilibria the wave equation with the variable phase speed reduces to the Klein-Gordon equation with constant coefficients. In this paper we apply the theory of non-reflective wave propagation to studying the Alfvén wave phase mixing in two-dimensional planar magnetic plasma equilibria. Using curvilinear coordinates we reduce the equation describing the Alfvén wave phase mixing to the equationthatbecomesaone-dimensionalwaveequationintheabsenceofdissipation.Thisequationisfurtherreducedtotheequation which is the one-dimensional Klein-Gordon equation in the absence of dissipation. Then we show that this equation has constant coefficients when a particular relation between the plasma density and magnetic field magnitude is satisfied. Using the derived Klein- Gordon-type equation we study the phase mixing in various non-reflective equilibria. We emphasise that our analysis is valid even when the wavelength is comparable with the characteristic scale of the background quantity variation. In particular, we study the Alfvén wave damping due to phase mixing in an equilibrium with constant plasma density and exponentially divergent magnetic field lines. We confirm the result previously obtained in the WKB approximation that there is enhanced Alfvén wave damping in this equilibrium with the damping length proportional to ln(Re), where Re is the Reynolds number. Our theoretical results are applied to heating of coronal plumes. We show that, in spite of enhanced damping, Alfvén waves with periods of the order of one minute can be efficiently damped in the lower corona, at the height about 200 Mm, only if the shear viscosity is increased by about 6 orders of magnitude in comparison with its value given by the classical plasma theory. We believe that such increase of the shear viscosity can be provided by the turbulence.

Professional interests

  • Applied mathematics
  • Linear and nonlinear waves
  • Astrophysics


  • Represents the HSE in other research organisations;
  • Organizes large academic events, including conferences, by the HSE in Nizhny Novgorod;
  • Supervises the development programme at the HSE in Nizhny Novgorod;
  • Presents the annual report on research activity and the HSE development strategy to the Academic Council.

Timetable for today

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A Strong Profile in IT and Humanities

The HSE Look talked to Anna Blyakhman, Deputy Director of HSE Nizhny Novgorod and Associate Professor at the Faculty of Management, about the educational programmes offered at the campus and its international students.

HSE Staff Members Awarded Status of Tenured Professor

On June 22, several HSE lecturers and staff members were awarded the status of Tenured Professor at a meeting of HSE Academic Council. Sixteen HSE staff members became Distinguished Professors at the Higher School of Economics for the first time.