Page 402 - Fundamentals of Magnetic Thermonuclear Reactor Design
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380 Fundamentals of Magnetic Thermonuclear Reactor Design
FIGURE A.12.2.1 Calculation scheme of PF coil on elastic supports.
FIGURE A.12.2.2 Current-carrying ring’s instability area in the toroidal field as function
4
3
of the supports’ stiffness. b* = IBR /a, Dimensionless load; с* = сR /a, dimensionless stiffness of
an elastic support.
Equations for the ring modelled as a Kirchhoff beam take the form
Q’+q=0, M’+t×Q=0, M’=a Q ′ += 0,q M ′ +×tQ = 0, M ′ =⋅a θ′, u ′ = θ′ × .t
⋅θ’, u’=θ×t. Here and further on, Q, M, θ and u are the vectors of force, moment, rotation
and displacement; prime denotes differentiation with respect to arc coordinate s;
q is the external loading intensity; a is the stiffness tensor; and t, n and k are the
stiffness tensor prime directions. The linear ponderomotive force, acting on the ring
I
qe=I×B=IBr′×e. q e =× B = IBr ′ × e ϕ .
In an undeformed coil, the current is parallel to the toroidal field, and this
force is zero. The force due to the ring deformation is a q variation caused by
e
displacement u
