Stabilizing Shells in ARIES

C. E. Kessel

Princeton Plasma Physics Laboratory

ARIES Project Meeting, 5/28-29/2008

Purpose of Stabilizing Shells in ARIES• Vertical Stability

– Elongated plasmas are unstable to vertical motion– Use conducting shells to slow the instability down– Feedback control coils can then hold the plasma’s vertical position– ARIES-AT, we had a 4 cm thick tungsten shell at about 0.33 times

the minor radius (measured from the plasma boundary) on the outboard side in the blanket

– Feedback control coils are located behind the shield but in front of the VV

• Kink Stability– In order to push plasma to high values a conducting shell is

required to help stabilize the plasma– The shell slows the instability down so that feedback coils can

control the instability, similar to the vertical instability– The requirements for this shell are much more difficult to assess– ARIES-AT, we had a 1 cm thick tungsten shell at the same location

as the vertical shell on the outboard side– Feedback control coils are located behind the shield but in front of

the VV

Vertical stability shell

Vertical feedback coils

Kink feedback coils

Kink stability shell

ARIES-AT(ceramic blanket)

ARIES-RS(Vanadium blanket)

Vertical stability shells

Vertical control coils

Kink shell is FW vanadium structure, 2 cm

Postulated that plasma might rotate fast enough for stabilization, no coils

Generic Vertical Stability Study from ARIES-AT

Surround plasma with conducting wall approx equidistant from plasma boundary, except in divertor regions

Analize effect of separation between plasma and conducting wall

Minimize wall poloidal coverage

Generic Vertical Stability Study from ARIES-AT

ARIES-AT had = 2.2, b/a = 0.33 ARIES-RS has = 1.9, b/a = 0.5

Scaling for Vertical Stabilization Shell

€

= 1.9 − 3.0(b

a Z− 0.45)

⎡

⎣ ⎢

⎤

⎦ ⎥1.2

f s

⎛

⎝ ⎜

⎞

⎠ ⎟

€

μoΔbη

≈ 0.25s

Assuming: feedback control coils are located behind sheildstructure is toroidally continuoushas the proper poloidal coverageshould check feedback control I and V

Feedback Control of Vertical Position

Analysis of the vertical control has been done with TSC to find I and V values, to give MVA requirement

The structure used in the analysis is whatever the final vertical shell design provides

The feedback control power available dictates how severe an instability can be before the plasma elongation or plasma current must be reduced

Feedback Control of the Vertical Position

Using final structure design

Using final structure parameters; resistivity (temperature) and material

Using final power limit from feedback simulations

Calculate vertical stability operating space as a function of current profile and pressure

If growth rate above 45 /s, need to lower elongation and/or plasma current

Kink Instability Shell

Placing conducting structures close enough to the plasma will slow the kink instability down, but not stabilize it

If the plasma is rotating and a damping mechanism exists then, the kink instability can be stabilized if the plasma rotates fast enough --- rotating large reactor plasmas is expected to be difficult

The alternative is to have feedback control coils to stabilize the plasma, and then plasma rotation is not required (we think) ---> this is our design choice

Only for rotating plasmas, the wall must be within this distance from the plasma

unstable

stable

Fast rotation Slower

rotation

Kink Stability ShellARIES-AT had N

max = 6.0, so the stabilizing wall must be placed at the location that stabilizes all the kink modes

ARIES-RS had Nmax = 5.4, and

the stabilizing shell had to be at b/a ≤ 0.25, however the actual location of the vanadium structure was at b/a ≈ 0.095 (at the FW)

The very close conductor is OK for feedback stabilization

Shell does NOT need to be toroidally continuous

Determining the maximum distance the kink shell can be from the plasma requires stability analysis

Kink Feedback Control

€

I = πZ Br /μoV = 3NμoRI /τ wτ w = μoΔb /η w

Br = smallest detectable perturbation (then assume that coil should produce 20-50 times this)

Z = height of coil above midplaneR = major radius of coilN = number of turns in coil

w = shell time constant (approx)= shell thicknessb = minor radial shell distancew = shell resistivity (function of T)

Leads and other parts of circuit are likely to make the coil performance worse, so keep w large and f small

w ≈ 3/2f, f ≈ 5 Hzw ≈ 0.1 s

If we assume the shell is close enough to the plasma and feedback coils are behind shield, then we can estimate its properties based on the feedback control

Stabilizing Shells in ARIES

• Vertical stability

– Formula relating elongation to vertical stabilizing shell location and stability factor

– Formula relating shell properties (distance, thickness, and resistivity) to an approximate time constant for vertical stability and control

• Kink stability

– Maximum location of stabilizing shell comes from stability analysis

– Formula relating shell properties (distance, thickness, and resistivity) to an approximate time constant for kink stability and control

• Feedback control requirements have not been identified