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Article information
2022 , Volume 27, ¹ 6, p.19-32
Kazakov E.A.
Two-mode model of a hydromagnetic dynamo with memory
The work addresses one of the directions for modelling of a mechanism of generation of large- scale magnetic fields for space objects — planets, stars, galaxies. The aim of the work is to derive and study small-scale dynamo models that describe at the phenomenological level the operation of two field generators, the so-called 𝛼- and 𝜔-effects. When changing the control parameters, the model can implement the main types of dynamos — 𝛼2, 𝛼𝜔, 𝛼2𝜔. All these types are found in real dynamo systems. Galerkin method was employed for derivation of the model from the equations of magnetohydro- dynamics. To prove the existence and uniqueness of the solution of the model, the method of contraction mappings was used. The study of various dynamic modes was carried out using numerical simulation. The article describes the derivation of the model equations from the general 𝛼2𝜔- dynamo equations in the mean field approximation. The suppression of the 𝛼-effect is provided by an integral term quadratic in the elements of the field, which introduces memory into the suppression mechanism. The quadratic form may describe the suppression of the 𝛼-effect by the helicity and/or energy of the field. The core of the suppression functional can be a rather arbitrary function. The choice of the kernel and the form of the quadratic form determines the specific suppression model. The existence and uniqueness of solutions of integro-differential equations of the model with arbitrary initial conditions on any finite time interval is proved. An implicit non-local difference scheme for numerical simulation is proposed. Numerical simulations were used to study various dynamic regimes arising in the model. When varying the control parameters, the model reproduces various dynamic modes typical of real space dynamo systems. The small dimension of the model allows simulating long-term dynamics on astronomical time scales.
[full text]
Keywords: Hydromagnetic dynamo, Galerkin approximations, low-mode dynamo models, memory (heredity)
doi: 10.25743/ICT.2022.27.6.003
Author(s):
Kazakov Evgeny Anatolievich
Position: Software Engineer
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SPIN-code: 3564-6783 References:
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Bibliography link:
Kazakov E.A. Two-mode model of a hydromagnetic dynamo with memory // Computational technologies. 2022. V. 27. ¹ 6. P. 19-32
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