The spontaneous magnetic field direction in an anisotropic MHD dynamo

The phenomenon of magnetic field generation in an astrophysical plasma in the frame of developed magnetohydrodynamic (MHD) turbulence is considered. The functional quantum field renormalization group approach is applied to helical anisotropic MHD developed turbulence which is stabilized by the self-generated homogeneous magnetic field. The purpose of the study is to calculate the value as well as direction of the magnetic field in the stochastic dynamo model. The generated magnetic field is determined by ignoring divergent rotor part of Green function of the magnetic field. It is shown that the magnetic field direction is connected with unique existing vector n describing the anisotropic turbulence forcing.Розглядається явище генерації магнітних полів в астрофiзичнiй плазмi у межах моделi розвиненої МГД-турбулентностi. Застосовується квантовопольовий пiдхiд ренормалiзацiйної групи до розвиненої гiротропно-анiзотропної турбулентностi, яка стабiлiзуєть ся самогенерованим магнiтним полем. Метою цього дослiдження є обчислення як значення, так i напрямку магнiтного поля у стохастичнiй моделі динамо. Генероване магнiтне поле визначається при знехтуваннi дивергентної роторної частини функцiї Грiна магнiтного поля. Показано, що напрямок магнiтного поля пов'язаний з наявністю вектора n, який описує анiзотропне накачування енергiї у турбулентнiсть.Рассматривается явление генерации магнитных полей в астрофизической плазме в рамках модели развитой МГД-турбулентности. Применяется квантовополевой подход ренормализационной группы к развитой гиротропно-анизотропной турбулентности, которая стабилизируется самогенерируемым однородным магнитным полем. Целью этого исследования является вычисление как значения, так и направления этого магнитного поля в стохастической модели динамо. Генерируемое магнитное поле определяется при пренебрежении дивергентной роторной частью функции Грина магнитного поля. Показано, что направление магнитного поля связано с наличием вектора n, описывающего анизотропное накачивание энергии в турбулентность

Stochastic magnetohydrodynamic turbulence in space dimensions d≥2d\ge 2

Interplay of kinematic and magnetic forcing in a model of a conducting fluid with randomly driven magnetohydrodynamic equations has been studied in space dimensions $d\ge 2$ by means of the renormalization group. A perturbative expansion scheme, parameters of which are the deviation of the spatial dimension from two and the deviation of the exponent of the powerlike correlation function of random forcing from its critical value, has been used in one-loop approximation. Additional divergences have been taken into account which arise at two dimensions and have been inconsistently treated in earlier investigations of the model. It is shown that in spite of the additional divergences the kinetic fixed point associated with the Kolmogorov scaling regime remains stable for all space dimensions $d\ge 2$ for rapidly enough falling off correlations of the magnetic forcing. A scaling regime driven by thermal fluctuations of the velocity field has been identified and analyzed. The absence of a scaling regime near two dimensions driven by the fluctuations of the magnetic field has been confirmed. A new renormalization scheme has been put forward and numerically investigated to interpolate between the $\epsilon$ expansion and the double expansion.Comment: 12 pages, 4 figure

Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy

Inertial-range scaling behavior of high-order (up to order N=51) structure functions of a passively advected vector field has been analyzed in the framework of the rapid-change model with strong small-scale anisotropy with the aid of the renormalization group and the operator-product expansion. It has been shown that in inertial range the leading terms of the structure functions are coordinate independent, but powerlike corrections appear with the same anomalous scaling exponents as for the passively advected scalar field. These exponents depend on anisotropy parameters in such a way that a specific hierarchy related to the degree of anisotropy is observed. Deviations from power-law behavior like oscillations or logarithmic behavior in the corrections to structure functions have not been found.Comment: 15 pages, 18 figure