Abstract
Two types of unstable eigenmodes of resistive tearing instabilities, namely, symmetric and anti-symmetric modes, in a double current sheet configuration are analyzed by means of both an eigenvalue solver and initial value simulation. It has been clearly identified that these two types of eigenmodes are different from the two independent single tearing modes even though the symmetric eigenmode in a double current sheet configuration shares the same properties of the single tearing mode near each current sheet. In the case with finite separation Δx between two current sheets, an arbitrary phase disturbance between two current sheets can lead to “phase instability,” i.e., the transition from the symmetric mode to the anti-symmetric mode. For a large Δx limit, both anti-symmetric and symmetric modes share the same properties of the single tearing mode. Thus, the superposition of two independent single tearing modes with arbitrary phases and arbitrary amplitudes at two current sheets can become the linear combination of symmetric and anti-symmetric eigenmodes. The same growth rate/eigenvalue of symmetric and anti-symmetric eigenmodes infers that an arbitrary superposition of two independent single tearing modes is still the eigenmode of the double current sheet configuration.
Highlights
Multiple current sheet configurations that form in solar coronal and solar wind plasmas,[1–3] Earth’s bow shock,[4,5] and advanced scenarios of fusion devices[6–8] are susceptible to magnetohydrodynamic instabilities, especially multiple tearing modes
It is clearly identified that the growth rate of the anti-symmetric mode (A-mode) is larger than that of the symmetric mode (S-mode), and the peak of the spectrum for the A-mode is located in a region of a relatively smaller wavenumber than that of the S-mode, i.e., kpyeakA < kpyeakS
The basic properties of the two types of the unstable modes, i.e., the A-mode and the S-mode in the double current sheet configuration are studied by means of both eigenvalue problem (EVP) and initial value problem (IVP) simulation
Summary
Multiple current sheet configurations that form in solar coronal and solar wind plasmas,[1–3] Earth’s bow shock,[4,5] and advanced scenarios of fusion devices[6–8] are susceptible to magnetohydrodynamic instabilities, especially multiple tearing modes. For a large Δx limit, both the A-mode and the S-mode become the special linear combinations of two single tearing modes with the same amplitude and fixed phase difference between two current sheets. They share the same properties of the two single tearing modes. The same growth rate/eigenvalue of the A-mode and the S-mode infers that any linear combination of two independent single tearing modes with arbitrary amplitudes and arbitrary phase differences at double current sheets is still the eigenmode of the system.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.