Ideal MHD Stability Boundaries of the PROTO-SPHERA Configuration

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Ideal MHD Stability Boundaries of the
PROTO-SPHERA Configuration F. Alladio, A.
Mancuso, P. Micozzi, F. Rogier Associazione
Euratom-ENEA sulla Fusione, CR Frascati C.P. 65,
Rome, Italy ONERA-CERT / DTIM / M2SN 2, av.
Edouard Belin - BP 4025 31055, Toulouse, France
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Spherical Tokamaks allow to obtain High
plasma current Ip (and high ltngt) with low BT
Plasma b much higher than Conventional Tokamaks
More compact devices
But, for a reactor/CTF extrapolation No
space for central solenoid (Current Drive
requirement more severe) No neutrons shield for
central stack (no superconductor/high dissipation)
Intriguing possibility ? substitute central rod
with Screw Pinch plasma
(ITF ? Ie)
Potentially two problems solved Simply
connected configuration (no conductors inside)
Ip driven by Ie (Helicity Injection from SP to ST)
Flux Core Spheromak (FCS) Theory Taylor
Turner, Nucl. Fusion 29, 219 (1989) Experiment
TS-3 N. Amemiya, et al., JPSJ 63, 1552 (1993)
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But Flux Core Spheromaks are injected by
plasma guns formed by 10 kV voltage on
electrodes high pressure prefilled with ST
safety factor q1
New configuration proposed PROTO-SPHERA Flux
Core Spherical Tokamak (FCST), rather than
FCS Disk-shaped electrode driven Screw Pinch
plasma (SP) Prolated low aspect ratio ST
(AR/a1.2, kb/a2.3) to get a Tokamak-like
safety factor (q01, qedge3) SP electrode
current Ie60 kA ST toroidal current Ip120240
kA ST diameter Rsph0.7 m ? Stability should
be improved and helicity drive may be less
disruptive than in conventional
Flux-Core-Spheromak
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PROTO-SPHERA formation follows TS-3 scheme (SP
kink instability)
Tunnelling (ST formation)
ST compression (Ip/Ie?, A ? )
T0 Ie8.5 kA
T3 Ip30 kA A1.8
T4 Ip60 kA A1.5
T5 Ip120 kA A1.3
T6 Ip180 kA A1.25
TF Ip240 kA A1.2
Ie 8.5?60 kA
Ip/Ie ratio crucial parameter (strong energy
dissipation in SP) MHD equilibria computed
both with monotonic (peaked pressure) as well
as reversal safety factor profiles (flat
pressure, µJB/B2 parameterized)
Some level of low n resistive instability
needed (reconnections to inject helicity from SP
to ST) but SPST must be ideally stable at any
time slice ? Ideal MHD analisys to assess Ip/Ie
ß limits
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Characteristics of the free-boundary Ideal MHD
Stability code
Plasma extends to symmetry axis (R0)
OpenClosed field lines Degenerate B0
Standard X-points
Boozer magnetic coordinates (?T,?,f) joined at
SP-ST interface to guarantee ?? continuity
inappropiate
Standard decomposition
like
but, after degenerate X-point (B0), ?T
? R0
??( )0 cannot be imposed
Solution ???RN (N1) ???B
?
Fourier analysis of
Normal Mode equation solved by 1D finite
element method
Kinetic Energy
Potential Energies
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Vacuum term computation (multiple plasma
boundaries)
Using the perturbed scalar magnetic potential F,
the vacuum contribution is expressed as an
integral over the plasma surface
Computation method for dWv based on 2D finite
element it take into account any stabilizing
conductors (vacuum vessel PF coil casings)
Vacuum contribution to potential energy not only
affect ?T contribution even to the
radial mesh points ?T and
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Stability results for time slices T3 T4
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?
Both times ideally stable ( gt0) for
n1,2,3 (q profile monotonic shear reversed)
Oscillations on resonant surfaces
Equilibrium parameters T3 Ip30 kA,
A1.8(1.9), ?2.2(2.4), q953.4(3.3),
q01.2(2.1), ßp1.15 and ß22(24) T4 Ip60 kA,
A1.5(1.6), ?2.1(2.4), q952.9(3.1),
q01.1(3.1), ßp0.5 and ß21(26)
Ip/Ie0.5
Ip/Ie1
T3
n1
n1
T4
ST
SP
ST
SP
ST
SP
ST
SP
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Stability results for time slices T5
With reference ßp0.3 ? n1 stable, n2 3
unstable
Equilibrium parameters T5 (monothonic q)
Ip120 kA, A1.3, ?2.1, q952.8, q01.0,
ß25 T5 (reversed q) Ip120 kA, A1.4,
?2.5, q953.5, q02.8, ß33
Ip/Ie2
ST drives instability only perturbed motion on
the ST/SP interface
Stability restored with ßp0.2
Equilibrium parameters T5 (monothonic q)
Ip120 kA, A1.4, ?2.2, q952.7, q01.2,
ß16 T5 (reversed q) Ip120 kA, A1.4,
?2.4, q952.7, q01.9, ß18
Stable oscillation on the resonant q surfaces
lt0
Monothonic q
Monothonic q
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Stability results for time slices T6
Screw Pinch drives instability ST tilt induced
by SP kink
With reference ßp0.225
Monothonic q ? n1 stable, n2 3
unstable Equilibrium parameters T6 Ip180 kA,
A1.25, ?2.2, q952.6, q00.96, ß25 Reversed
q ? n1, n2 3 unstable Equilibrium
parameters T6 Ip180 kA, A1.29, ?2.5,
q953.2, q02.3, ß33
-6.810-4
Ip/Ie3
Weak effect of vacuum term for n1
-6.810-4 ? -710-4 if PF coil casings suppressed
With lower ßp0.15
Monothonic q ? n1,2,3 stable Equilibrium
parameters T6 Ip180 kA, A1.29, ?2.2,
q952.5, q01.12, ß15 Reversed q ? n1,2,3
stable Equilibrium parameters T6 Ip180 kA,
A1.32, ?2.5, q952.5, q01.83, ß19
Reversed q
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Stability results for time slices TF
Screw Pinch drives instability ST tilt induced
by SP kink (kink more extended with respect to T6)
With reference ßp0.225
Monothonic q ? n1 stable, n2 3
unstable Equilibrium parameters TF Ip240 kA,
A1.22, ?2.2, q952.65, q01.04, ß19 Reversed
q ? n1 2 unstable, n3 stable Equilibrium
parameters TF Ip240 kA, A1.24, ?2.4,
q952.89, q01.82, ß23
-1.510-3
Ip/Ie4
With lower ßp0.12 Monothonic q ? n1,2,3
stable Equilibrium parameters TF Ip240 kA,
A1.24, ?2.3, q952.55, q01.13, ß16 With
further lowered ßp0.10 Reversed q ? n1,2,3
stable Equilibrium parameters TF Ip240 kA,
A1.26, ?2.4, q952.55, q01.64, ß14
Reversed shear profiles less effective in
stabilizing SP kink
Reversed q
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Effect of ST elongation on Ip/Ie limits
gt0
PROTO-SPHERA (b/a3) Stable for
n1,2,3 Equilibrium parameters Ip329
kA Ie60 kA A1.23 ?3.0 q952.99, q01.42
ß13 (monothonic q)
Increasing ? allow for higher Ip/Ie ratio
Ip/Ie5.5
PROTO-SPHERA (standard b/a) Unstable for
n1 Stable for n2 3 Equilibrium
parameters Ip300 kA Ie60 kA
A1.20 ?2.3 q952.7, q01.15
ß15 (monothonic q)
Ip/Ie5
-4.410-2
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Comparison with TS-3 (1)

• Tokio Device had
• Simple linear electrodes
• Oblated Spherical Torus
• qlt1 all over the ST (Spheromak)

Ip50 kA, Ie40 kA Ip/Ie1 , A1.8
Ip100 kA, Ie40 kA Ip/Ie2 , A1.5
Code confirms experimental results
n1
n1
gt0
Stable q1 resonance
Strong SP kink, ST tilt
-1.05
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Comparison with TS-3 (2) (effect of the SP shape)
T5 (ß16) Ip120 kA, Ie60 kA Ip/Ie2 , A1.3
T5-cut (ß16) Ip120 kA, Ie60 kA Ip/Ie2 , A1.3
n1
n1
If the fully stable T5 is artificially cut to
remove degenerate X-points as well as disk-shaped
SP ? Strong n1 instability
appears, despite higher ? q95
gt0
Stable q3 resonance
Strong SP kink, ST tilt
-0.17
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Conclusions
Ideal MHD stability results for
PROTO-SPHERA PROTO-SPHERA stable at full ß
2126 for Ip/Ie0.5 1, down to 1416 for
Ip/Ie4 (depending upon profiles inside the ST)
Comparison with the conventional Spherical
Tokamak with central rod ßT02829 for
Ip/Ie0.5 to ßT07284 for Ip/Ie4 Spherical
Torus dominates instabilitiy up to Ip/Ie3
beyond this level of Ip/Ie, dominant
instability is the SP kink (that gives rise to ST
tilt motion) Spherical Torus elongation ?
plays a key role in increasing Ip/Ie
Comparison with TS-3 experimental results
disk-shaped Screw Pinch plasma important for the
configuration stability
Ideal MHD stability of Flux Core Spherical Torus
rather insensitive to internal ST profiles ?
configuration quite robust from an ideal point of
view Resistive instabilities behaviour is the
main experimental point of PROTO-SPHERA