Page 6 - Microsoft PowerPoint - Galkin-APS-DPP-2020-talkFinal

Reduced MHD model ( 2D, cylindrical )
𝜕𝛺 𝑣􏰁 𝛺 𝐵􏰁 =−𝒗􏰀𝛻𝛺+ +𝜌𝑩􏰀𝛻𝑗􏰂 −
𝜕𝑗􏰂=−∆􏰂 (𝒗×𝑩)􏰂−𝜂𝑗􏰂 /𝜇􏰃 𝜕𝑡
𝜌𝑗􏰂 −𝑗􏰂𝑩􏰀𝛻𝜌
𝜕𝑡 𝑟 𝑟
𝑀
𝑑𝐼􏰄􏰅􏰆 𝑑𝑡
= −𝑅𝐼􏰄􏰅􏰆 −
𝜕Ψ𝑝 𝜕𝑡
+ 𝑈􏰄􏰅􏰆
Ω=ρ2𝛻 × 𝑣 𝑗􏰂
Iext
ρ
Generalized vorticity Plasma current density Magnets and wall currents Plasma mass density
P R I V I L E G E D A N D C O N F I D E N T I A L 6
𝜕𝜌 = −𝒗􏰀𝛻𝜌 𝜕𝑡
Presenter: Sergei Galkin