On violent instability of a plasma-vacuum interface for an incompressible plasma flow and a nonzero displacement current in vacuum

Standard

On violent instability of a plasma-vacuum interface for an incompressible plasma flow and a nonzero displacement current in vacuum. / Trakhinin, Yuri.

In: Communications in Mathematical Sciences, Vol. 18, No. 2, 01.02.2020, p. 321-337.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{89324c1cf1ed4b90956c50dc5e22204e,

title = "On violent instability of a plasma-vacuum interface for an incompressible plasma flow and a nonzero displacement current in vacuum",

abstract = "In the classical statement of the plasma-vacuum interface problem in ideal magnetohydrodynamics (MHD) one neglects the displacement current in the vacuum region that gives the div-curl system of pre-Maxwell dynamics for the vacuum magnetic field. For understanding the influence of the vacuum electric field on the evolution of a plasma-vacuum interface we do not neglect the displacement current and consider the full Maxwell equations in vacuum. For the case of an incompressible plasma flow, by constructing an Hadamard-type ill-posedness example for the constant coefficient linearized problem we find a necessary and sufficient condition for the violent instability of a planar plasma-vacuum interface. In particular, we prove that as soon as the unperturbed plasma and vacuum magnetic fields are collinear, any nonzero unperturbed vacuum electric field makes the planar interface violently unstable. This shows the necessity of the corresponding non-collinearity condition for well-posedness and a crucial role of the vacuum electric field in the evolution of a plasma-vacuum interface.",

keywords = "Free boundary problem, Ideal incompressible magnetohydrodynamics, Ill-posedness, Plasma-vacuum interface",

author = "Yuri Trakhinin",

year = "2020",

month = feb,

day = "1",

doi = "10.4310/CMS.2020.v18.n2.a2",

language = "English",

volume = "18",

pages = "321--337",

journal = "Communications in Mathematical Sciences",

issn = "1539-6746",

publisher = "International Press of Boston, Inc.",

number = "2",

}

RIS

TY - JOUR

T1 - On violent instability of a plasma-vacuum interface for an incompressible plasma flow and a nonzero displacement current in vacuum

AU - Trakhinin, Yuri

PY - 2020/2/1

Y1 - 2020/2/1

N2 - In the classical statement of the plasma-vacuum interface problem in ideal magnetohydrodynamics (MHD) one neglects the displacement current in the vacuum region that gives the div-curl system of pre-Maxwell dynamics for the vacuum magnetic field. For understanding the influence of the vacuum electric field on the evolution of a plasma-vacuum interface we do not neglect the displacement current and consider the full Maxwell equations in vacuum. For the case of an incompressible plasma flow, by constructing an Hadamard-type ill-posedness example for the constant coefficient linearized problem we find a necessary and sufficient condition for the violent instability of a planar plasma-vacuum interface. In particular, we prove that as soon as the unperturbed plasma and vacuum magnetic fields are collinear, any nonzero unperturbed vacuum electric field makes the planar interface violently unstable. This shows the necessity of the corresponding non-collinearity condition for well-posedness and a crucial role of the vacuum electric field in the evolution of a plasma-vacuum interface.

AB - In the classical statement of the plasma-vacuum interface problem in ideal magnetohydrodynamics (MHD) one neglects the displacement current in the vacuum region that gives the div-curl system of pre-Maxwell dynamics for the vacuum magnetic field. For understanding the influence of the vacuum electric field on the evolution of a plasma-vacuum interface we do not neglect the displacement current and consider the full Maxwell equations in vacuum. For the case of an incompressible plasma flow, by constructing an Hadamard-type ill-posedness example for the constant coefficient linearized problem we find a necessary and sufficient condition for the violent instability of a planar plasma-vacuum interface. In particular, we prove that as soon as the unperturbed plasma and vacuum magnetic fields are collinear, any nonzero unperturbed vacuum electric field makes the planar interface violently unstable. This shows the necessity of the corresponding non-collinearity condition for well-posedness and a crucial role of the vacuum electric field in the evolution of a plasma-vacuum interface.

KW - Free boundary problem

KW - Ideal incompressible magnetohydrodynamics

KW - Ill-posedness

KW - Plasma-vacuum interface

UR - http://www.scopus.com/inward/record.url?scp=85086342685&partnerID=8YFLogxK

U2 - 10.4310/CMS.2020.v18.n2.a2

DO - 10.4310/CMS.2020.v18.n2.a2

M3 - Article

AN - SCOPUS:85086342685

VL - 18

SP - 321

EP - 337

JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

SN - 1539-6746

IS - 2

ER -

ID: 24518210