1. Stabilizing Shells in ARIES C. E. Kessel Princeton Plasma Physics Laboratory ARIES Project Meeting, 5/28-29/2008

2. 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

3. Vertical stability shell Vertical feedback coils Kink feedback coils Kink stability shell ARIES-AT (ceramic blanket)

4. 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

5. 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

6. Generic Vertical Stability Study from ARIES-AT ARIES-AT had  = 2.2, b/a = 0.33ARIES-RS has  = 1.9, b/a = 0.5

7. Scaling for Vertical Stabilization Shell Assuming: feedback control coils are located behind sheild structure is toroidally continuous has the proper poloidal coverage should check feedback control I and V

8. 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

9. 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

10. 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

11. Kink Stability Shell ARIES-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  N max = 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

12. Kink Feedback Control B r = smallest detectable perturbation (then assume that coil should produce 20-50 times this) Z = height of coil above midplane R = major radius of coil N = number of turns in coil  w = shell time constant (approx)  = shell thickness b = minor radial shell distance  w = 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 ≈ 3/2  f, f ≈ 5 Hz  w ≈ 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

13. 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