Linear stability analysis of a hot plasm
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Linear stability analysis of a hot plasm
Linear stability analysis of a hot plasm
arXiv: 1308.1177vl [math.AP] 6 Aug 2013Linear Stability Analysis of a Hot Plasma in a Solid Torus*Toaii T. Nguyen' Walter A. Strauss*41493AbstractThis Linear stability analysis of a hot plasms paper is a first step toward understanding the effect of toroidal geometry on the rigorous stability theory of plasmas. We consider a collisionless plasma inside a torus, modeled by the relativistic Vlasov-Maxwell system. The surface of the toms is perfectly conducting and it reflects the particle Linear stability analysis of a hot plasms specularly. We provide sharp criteria for the stability of equilibria under the assumption that the particle distributions and the electromagnetic fLinear stability analysis of a hot plasm
ields depend otdy on the cross-sectional variables of the torus.Contents1Introduction21.1Toroidal symmetry............................................arXiv: 1308.1177vl [math.AP] 6 Aug 2013Linear Stability Analysis of a Hot Plasma in a Solid Torus*Toaii T. Nguyen' Walter A. Strauss*41493AbstractThis Linear stability analysis of a hot plasm.................................... 61.4Main results................................................................... 82Thesymmetric system92.1The equations in toroidal coordinates.......................................... 92.2Boundary conditions................................................... Linear stability analysis of a hot plasm........ 102.3Linearization................................................................. 112.4The Vlasov operators................................Linear stability analysis of a hot plasm
.......................... 122.5Growing modes................................................................. 132.6Properties of £° .................arXiv: 1308.1177vl [math.AP] 6 Aug 2013Linear Stability Analysis of a Hot Plasma in a Solid Torus*Toaii T. Nguyen' Walter A. Strauss*41493AbstractThis Linear stability analysis of a hot plasm3.2Growing modes are pure........................................................ 163.3Minimization.................................................................. 183.4Proof of stability............................................................ 21’Department of Mathematics, Pennsylvania Stale U Linear stability analysis of a hot plasmniversity, University Park, PA 16802, USA. Email: nguyenOmath.pBU.edu.’Department of Mathematics anil Lcfschclz Center for Dynamical Systems. Brown UnLinear stability analysis of a hot plasm
iversity. Providence, III 02912, USA. Email: wstraussOmath.brown.edu.‘Research of the authors was supported in part by the NSF under grants DMS-110882arXiv: 1308.1177vl [math.AP] 6 Aug 2013Linear Stability Analysis of a Hot Plasma in a Solid Torus*Toaii T. Nguyen' Walter A. Strauss*41493AbstractThis Linear stability analysis of a hot plasmov-Maxwell system is assumed to be valid inside a solid torus (see Figure 1), which we take for simplicity to beíĩ = Ịx = (£I,X2,£3) € R3 : (a-++ *3 < 1Ị.The specular condition at the boundary is/±(t,x,v) = /±(í,x,t.’- 2(t? ■ n(a-))n(j)),n(z)-v<0, X G ỚÍÌ, (1.4)where n(x) denotes the outward normal Linear stability analysis of a hot plasmvector of ỚÍỈ at X. The perfect conductor boundary condition isE(t,x) X n(x) = 0, B(t,x) • n(x) = 0, X e dLinear stability analysis of a hot plasm
hese boundary conditions is that the total energyi(t) = f f mr+r )+1 (|E|2+|B|2) dxarXiv: 1308.1177vl [math.AP] 6 Aug 2013Linear Stability Analysis of a Hot Plasma in a Solid Torus*Toaii T. Nguyen' Walter A. Strauss*41493AbstractThisarXiv: 1308.1177vl [math.AP] 6 Aug 2013Linear Stability Analysis of a Hot Plasma in a Solid Torus*Toaii T. Nguyen' Walter A. Strauss*41493AbstractThisGọi ngay
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