Plasma Stability in Alternate Confinement Concepts
Lawrence Livermore National LaboratoryLivermore, CA 94526
Global Climate & Energy Project WorkshopPrinceton
May 1-2, 2006
Work performed under the auspices of the U. S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.
E. Bickford Hooper
UCRL-PRES-220891
I am pleased to thank many colleagues, including:
Per Brunsell
Rick Ellis
Adil Hassam
Dan Den Hartog
Alan Hoffman
Jay Kesner
Harry McLean
Dick Post
Dmitri Ryutov
John Sarff
Uri Shumlak
Any misinterpretations or errors are my responsibility
A wide range of Innovative Confinement Concepts (ICCs) contribute to the physics of plasmas and fusion-energy
Macroinstabilities and microinstabilities may be present
Macroinstabilities are large scale and usually described by fluid models, e.g. Magnetohydrodynamics (MHD)
Microinstabilities are fine scale (typically with wavelengths comparable to the ion Larmor radius) and usually require kinetic descriptions
This presentation focuses on macroinstabilities in ICCs
These studies of stability complement those in tokamaks and stellarators
Control of instabilities will be essential for any ICC reactor
Magnetic confinement devices have either toroidal or open magnetic field lines with the plasma weakly or highly constrained
Highly ConstrainedTandem MirrorGas Dynamic Trap
Weakly ConstrainedZ-pinchCentrifugal Confinement
Highly ConstrainedTokamak*Spherical Torus (ST)*Stellarator*Levitated Dipole
*The stability of the tokamak, ST, and stellarator are not discussed here
Self-OrganizedReversed-Field Pinch (RFP)SpheromakField-Reversed Configuration (FRC)
Toroidal
Open
TOROIDAL SYSTEMS
RFP Low toroidal field makes safety factor q
Standard RFP operation: A spectrum of tearing modes develops through instability and nonlinear coupling.
0 10 20 30
1%
0
Toroidal Mode, n
B ( a ) / B
inner-most resonantm = 1, n = 6 B / B ~ 1%
Nonlinear coupling between the modes leads to sawteeth dynamo events in which poloidal flux injected by the ohmic transformer is converted into toroidal flux
The spectrum spans a wide range of toroidal mode numbers (n)
Electron heat transport in standard RFP agrees well with stochastic magnetic expectations.
e(m2/s)
r/a
measuredpower-balance
R-R
Toro
idal
,
directly from field line tracing
RR = vTeDm
Dm = r2 /L
predicted Rechester-Rosenbluth
Field line tracing:
use measured equilibrium B(r)
fluctuation B(r) from nonlinear MHDcomputation using measured (r) andLundquist number (S 106)
normalize B(r) to measured B(a)(< 2X correction required)
~~
~
magneticdiffusivity
Field line puncture plotFluctuations generate stochasticity
0 10 20 30Time (ms)
1.0
0.5
0
B rms(%)
1021027066
~
0
0.04
0.08
B(a)(T)
Standard
PPCD
Pulsed Poloidal (inductive) Current Drive (PPCD) targeted to outer-plasma region reduces MHD tearing instability.
(m2/s)
r/a
power balance
R-R1
10
100
1000
The poloidal current (and toroidal field) are transiently reduced
0.2
0.4
0.6
0.8
1.0
Te(KeV)
0 0.2 0.4 0.6 0.8 1r/a
Standard
PPCD-Improved
The peak electron temperature increases significantly
Field line puncture calculations show large areas of good surfaces
On the resistive-time of the conducting shell, external kink modes become resistive-wall modes
Feedback control has been demonstrated on EXTRAP-T2R
RFP: Summary
m = 1 resistive tearing modes develop at mode-rational surfaces, q = 1/n
These modes grow to sufficiently large amplitudes that their islands overlap and the magnetic field becomes stochastic
The electron thermal conductivity is large, the electron temperature profile flat and peak Te low
PPCD changes the current and electric field profiles
Mode amplitudes are significantly reduced and good flux surfaces are calculated in much of the volume
The electron-temperature profile becomes peaked and Te is increased by ~ 3
On the resistive time of the wall, feedback stabilization reduces the RWM amplitudes significantly
The discharge duration is lengthened by a factor of 3
MHD stability in the gun-injected spheromak
A large current is driven from the inner electrode to the flux conserver
Following formation, the current flows through the donut-hole, forming a column which pinches as shown
The spheromak lies inside the separatrix, shown in red
Good energy confinement is found when magnetic surfaces are closed
Closed surfaces require low magnetic fluctuation levels
1 m
SSPX (Sustained Spheromak Physics Experiment) a coaxial helicity-injected confinement experiment
MHD stability in the gun-injected spheromak
= 0 j / B
Magnetic fluctuations occur due to MHD modes:
On the column (outside the separatrix) where the current profile is similar to a z-pinch
The n=1 column mode drives current in the spheromak
The column mode is stabilized for where
and In the spheromak (inside the separatrix)
Internal modes occur on low-order rational surfaces, q = m/n
Generally, 0.5 q 1 Experimentally, best stability occurs
when the q-profile lies between 1/22/3
B = fcB 1< < 1.5 gun fc
Experiment: low fluctuations with low edge , no low-order rational surfaces
The n=1 column mode reaches large amplitude (B/B~10%). Nonlinear processes drive magnetic reconnection events which converts injected toroidal flux into poloidal flux
The reconnection events generate voltage spikes on the gun, seen both in experiment and in resistive MHD simulations
The n=1 column mode dominates the spectrum
The poloidal magnetic field and flux increase with each event
Modeling and experiment show a consistent picture of the physics processes during spheromak formation and
sustainment
Te(experiment) is low during strong n=1 activity modeling (above) shows the magnetic surfaces opening in each event, dropping Te
A strong n=1 mode develops during spheromak buildup and
sustainment at high gun current
E. B. Hooper, et al., Phys. Plasmas 12, 092503 (2005).
Internal modes in the experiment are found to occur when the q-profile crosses low-order rational surfaces
Magnetic fluctuations correlate with the reconstructed q-profile
Shown is the observed spectrum together with the maximum and minimum in the q-profile
The q-profile is sensitive to the ratio of gun current to gun flux
Safety-factor scaling with
edge = 0Igun/gun
Good energy confinement is found when the q-profile has no low-order rational surfaces
H. S. McLean, Phys. Plasmas (to be published).
Spheromak: Summary
The n=1 column mode drives current via a dynamo
Injected toroidal flux is converted into poloidal flux by a reconnectionevent
The reconnection event opens magnetic flux surfaces allowing a large thermal conductivity to the walls
This large heat leak will require separation of the current drive phase from a reactor burn phase a pulsed or refluxed spheromak is probably required
Internal modes amplitudes are small when the q-profile does not span the 1/2 or 2/3 surface
Simulations find a similar effect, with poor confinement resulting when magnetic fluctuations generate islands or stochastic field lines
Good energy confinement in a reactor may require current-profile control to shape the q-profile and maintain mode amplitudes < 1%
FRC Macrostability stability
rc rsBo
Be
s
Bi
Stability depends on the geometry [prolate (shown) or oblate], external conducting wall, external magnetic mirror ratio, and other features
The ideal FRC has no current along B and thus has no current-driven, MHD modes (pressure-driven only)
Local ideal modes (n>>1) interchange, co-interchange (ballooning) are predicted to be unstable but usually not observed
Stabilized by conducting shell, external magnetic mirror, etc.
Global ideal modes in absence of rotation (n=0, 1, >1) axial shift, sideway shift, tilt may be theoretically unstable but have not been observed
Global ideal modes driven by rotation have been observed
Resistive tearing modes have been observed during formation
Refs.: M. Tuszewski, Nucl. Fusion 28, 2033 (1988); H. Ji et al., Phys. Plasmas 5, 3685 (1998).
FRC Dominant global instability is usually the n=2, rotating interchange mode
n=2 rotating interchange Driven by centrifugal force
due to plasma rotation. Observed experimentally
in most FRCsEnd
View
Side View
Usually stabilized by external static multipole fields in -pinch formed FRCs.
Instability not seen in translated FRCs due to development of moderate toroidal field and high shear.*
Instability is stabilized by Rotating Magnetic Fields (RMF).**
Finite Larmor-radius effects are usually stabilizing.***
*H. Guo, et al., Phys. Rev. Letters 95, 175001 (2005).
** H. Guo, et al., PRL 94, 185001 (2005).
***E. Belova, et al., Phys. Plasmas 11, 2361 (2003
