Skip to main content
SpringerLink
Log in

An Efficient Algorithm for Calculating the Magnetic Field in a Cylindrical Plasma Trap

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this work, we propose a numerical algorithm for calculating the magnetic field in an open magnetic trap, which is an axisymmetric chamber filled with plasma. The plasma is held in the trap by a special configuration of the magnetic field generated by current coils located at the ends of the chamber. The problem consists in developing an efficient algorithm for calculating the configuration of the magnetic field, which is determined by a given distribution of the external azimuthal current in the coils. The task is solved in two steps. First, the magnetic field distribution is found from the known arrangement of coils, and then this distribution is scaled so that the magnitude of the field in the center of the chamber and the mirror ratio are equal to the given values. The proposed algorithm can be easily generalized to solve the Poisson equation with Neumann boundary conditions on two opposing boundaries of the computational domain. This allows us to apply the developed method to calculate the potential in nonstationary problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Notes

  1. Note that on the axis of the trap the magnetic field has only \(z\)-component \(B_{z}.\)

  2. Due to the central differences in (10), the boundary conditions (6), (7), and (8) are approximated with second order.

REFERENCES

  1. V. M. Verzhbitsky, Foundations of Numerical Methods (Vyssh. Shkola, Moscow, 2002) [in Russian].

    Google Scholar 

  2. C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (CRC, Boca Raton, 2004).

    Google Scholar 

  3. F. F. Chen, Introduction to Plasma Physics and Controlled Fusion (Springer, Cham, 2016).

    Book  Google Scholar 

  4. Yu. A. Beresin, G. I. Dudnikova, T. V. Liseykina, and M. P. Fedoruk, Modeling of Unsteady Plasma Processes (Novosib. Gos. Univ., Novosibirsk, 2018) [in Russian].

    Google Scholar 

  5. A. D. Beklemishev, ‘‘Diamagnetic ‘bubble’ equilibria in linear traps,’’ Phys. Plasmas 23, 082506 (2016).

  6. V. D. Shafranov and A. V. Timofeev, ‘‘Magnetic traps,’’ in Great Russian Encyclopedia (Moscow, 2011), Vol. 18, pp. 376–377 [in Russian].

Download references

Funding

Authors acknowledge the financial support by Russian Science Foundation within grant no.  19-71-20026.

Author information

Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, 630090, Novosibirsk, Russia

    T. V. Liseykina & V. A. Vshivkov

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    U. A. Kholiyarov

Authors
  1. T. V. Liseykina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Vshivkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. U. A. Kholiyarov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to T. V. Liseykina, V. A. Vshivkov or U. A. Kholiyarov.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

(Submitted by A. B. Muravnik)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liseykina, T.V., Vshivkov, V.A. & Kholiyarov, U.A. An Efficient Algorithm for Calculating the Magnetic Field in a Cylindrical Plasma Trap. Lobachevskii J Math 45, 75–84 (2024). https://doi.org/10.1134/S1995080224010359

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080224010359

Keywords:

Search

Navigation