Topics in Fusion and Plasma Studies 2 (459.667)

Midterm Examination

6 November, 2009

1. The Shafranov shift is expressed as follows,

,

(1) Fill in 가, 나 and explain the meaning of this equation with them.

(2) Calculate how much vertical field is needed to keep the plasma centered.

(3) If the plasma is elongated, how should the vertical field be modified?

Explain this with a simple cartoon and a criterion which the vertical field should satisfy.

2. Consider the standard form of the fluid energy derived from the energy principle (a) and the boundary terms (b) as shown below. Describe the physical meaning of each term in (a) and describe the meaning of (b).

(a)

,                        (b)

3. (1) What is the stability criterion for the internal pressure-driven modes in a straight tokamak correspond to localised interchange instabilities?

(2) Assume q(r), q'(r) and p'(r) can be replaced by q0, q0''r, and p0''r, resectively, what is the requirement of the pressure profile for the stability in the vicinity of the axis?

(3) Consider the Mercier criterion of noncircular cross sections as described below,

.

Discuss the effect of elongation, triangularity, poloidal beta to the stability condition.

(4) Why are the elongated D-shapes preferable in tokamak plasmas?

4. Evaluate ωi for the m=2, n=1 resistive wall mode in KSTAR using the information as following; R=1.8m, a=0.5m, b=2.5m, d=0.01m, η=11x10-8Ωm, μ0=1200nHm-1, Bz=3.5T (uniform), k0=1, ξa=1, ξa'=2.

5. (1) Plot an ideal q-profile which satisfies all the ideal MHD stability conditions for a tokamak and explain.

(2) With respect to tokamak operations, which stability criteria do make limitations on plasma current and plasma beta?

“The LORD is my shepherd, I shall not be in want.

He makes me lie down in green pastures, he leads me beside quiet waters,

he restores my soul. He guides me in paths of righteousness for his name's sake.

Even though I walk through the valley of the shadow of death, I will fear no evil, for you are with me; your rod and your staff, they comfort me.“ (Psalms 23:1-4)