1European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Experimental RFP results
Emilio Martines
Consorzio RFX, Padova, Italy
email: [email protected]
2European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Outline
A bit of history
Magnetic configuration
Discharge formation
Dynamo
PPCD-OPCD
Oscillating Field Current Drive (OFCD)
Transport mechanisms
Scaling laws
The shell problem
Mode locking
Advanced RFP: the Single Helicity paradigm
Density limit
3European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
A bit of history: ZETA
25th January 1958
In the last operation phase some shots revealed a "quiescent period" of long stability in a system that otherwise appeared to prove itself unstable.
This quiescent phase was characterized by a reversed toroidal field at the wall RFP !
E.P. Butt et al., 2nd IAEA Fusion Energy Conference, Culham, vol. 2, p. 751 (1965).D.C. Robinson et al., 3rd IAEA Fusion Energy Conference, Novosibirsk, vol. I, p. 263 (1968).
Quiescent phase
“Pinch device”. Operational from 1954 to 1968.
R = 1.5 m, a = 0.5 m, Ip = 800 kA.
4European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
A bit of history: 40 years of RFP research
Padova (Italy)
Culham (UK)
Los Alamos (USA)
Tsukuba (Japan)
Nagoya (Japan)
San Diego (USA)
Tokyo (Japan)
Stockholm (Sweden)
Chengdu (China)
Madison (USA)
1st gen. (‘70s)
ETA BETA I
HTBX-1
ZT-1
TPE-1R, R(M)
STP-1(M)
-
-
-
-
-
2nd gen. (‘80s)
ETA BETA II
HTBX-1B, 1C
ZT-40, ZT-40M
TPE-1RM20, TPE-2M
STP-3(M)
OHTE
REPUITE-1
Extrap-T1
SWIP-RFP
-
3rd gen. (‘90s)
RFX, RFX-mod
-
ZTH (canceled)
TPE-RX
-
-
RELAX
Extrap-T2
-
MST
In red the experiments presently in operation.
5European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
A bit of history: 40 years of RFP research
1st generation (‘70s): Small machines with non-conducting first wall and very fast current rise.
2nd generation (‘80s): Small machines with conducting wall, and slower current rise, motivated by Taylor’s theory of relaxation.
3rd generation (‘90s to present): Larger machines with higher plasma current (RFX: 2 MA, TPE-RX: 1 MA, MST: 0.55 MA)
6European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Magnetic configuration: F- plot
The RFP state is often described through the pinch parameter and the reversal parameter F.
Experimental points are found to lie on a well-defined curve on the F- plane.
B
)a(BF
B
)a(B
If the operator determines given values of plasma current and toroidal field at the edge, the plasma will adjust the toroidal flux so as to lie on the F - curve.
H.A.B. Bodin, A.A. Newton, NF 20, 1255 (1980)
7European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Magnetic configuration: F- plot
The curve in the F- plane is also followed during the discharge formation in every shot, regardless of the reached plasma current.
F
t (s)
Ip (MA)
8European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Magnetic configuration: RFP profiles
The RFP magnetic field profiles have been measured in ETA BETA II using insertable pick-up coils at Ip ~ 100 kA and ~ 1.9.
The reconstructed q profile confirms that q(0) ~ 2a/3R.
The profile is flat only in the core, and decreases towards the edge.
V. Antoni et al., PPCF 29, 279 (1987)V. Antoni et al., NF 29, 1759 (1989)
9European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Magnetic configuration: RFP profiles
The magnetic field profiles have been measured by insertable pick-up coils also in HTBX.
H.A.B. Bodin, IAEA Fusion Energy Conference, Lausanne, vol. 1, p. 417 (1984)
10European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Discharge formation: Self and aided reversal
The first RFP plasma were obtained by “self-reversal”, that is exploiting the presence of a toroidal flux conserver (either the shell or the toroidal field coils). This is still possible in modern machines, by short-circuiting the toroidal field coils when the plasma current is started. However, the most usual approach is to aid the reversal by reversing the current in the toroidal field coils, and then sustain this current to chosen level.
self-reversal
aided reversal
RFX-modshots 23287, 20276
11European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Discharge formation: Different start-up scenarios
Three basic start-up types:• Ramped: reversal happens early, then Ip is raised in a RFP state, increasing the toroidal flux.• Aided: the toroidal flux is reduced by the discharge formation• Matched: the toroidal flux is kept constant
15978 Ramped15962 Matched15938 Aided
12European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Discharge formation: Different start-up scenarios
According to Sprott’s 0D modeling, the ramped scenario is the most expensive and the aided one is the most economic in terms of volt-second consumption (stored magnetizing flux).
In practice, flux consumption is much larger than expected because of resistive losses (ignored in Sprott’s model). The different start-up modes appear to be not so different in terms of volt-second consumption
J. C. Sprott, Phys, Fluids 31, 2266 (1988).
13European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Dynamo: Basic concept
jBvE ~~
m = 1 MHD modes
The poloidal current in the RFP is sustained against resistive diffusion, which would tend to flatten the toroidal field profile, by the non-linear effect of m=1 tearing modes which are resonant inside the reversal surface. This process is called dynamo.These modes are therefore intrinsic to the configuration.
14European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Dynamo: Measurement of the dynamo field
In MST the dynamo acts in bursts, called Discrete Relaxation Events (true also in RFX, but only at deep reversal).The MHD dynamo term in Ohm’s law has been measured, and turns out to be consistent with expectations in the edge. Deeper inside, an additional Hall term has to be invoked.
P.W. Fontana et al., PRL 85, 566 (2000)W.X. Ding, PRL 93, 045002 (2004)
15European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Pulsed Poloidal Current Drive (PPCD)
The PPCD technique, for transiently reducing magnetic fluctuations and improving confinement, was pioneered by the MST group. The rationale is to “help” the dynamo by inducing a poloidal current through a sudden decrease of the toroidal field at the wall.A poloidal beta of 15% and a tenfold increase of confinement time (up to 10 ms) in sawtooth-free plasmas have been achieved by this method.
J.S. Sarff, PRL 72, 3670 (1994)B. Chapman, PRL 87, 205001 (2001)
16European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Pulsed Poloidal Current Drive (PPCD)
Equilibrium reconstruction with many constraints, including Faraday rotation, motional Stark effect, Thomson scattering and interferometry.
The MST experiments demonstrate that PPCD suppresses the dynamo (the applied electric field matches the current density), and induces a transition from a Multiple Helicity state to a state with one or two dominant modes, as shown by tomographic reconstructions.
S.C. Prager et al., NF 45, S276 (2005)
Standard PPCD
17European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Pulsed Poloidal Current Drive (PPCD)
An enhanced hard X-ray spectrum, attributed to high energy electrons, is observed in MST during PPCD, together with a reduction of magnetic fluctuations. This suggests that core transport may not be due any more to magnetic field line ergodicity.
R. O’Connell et al., PRL 91, 045002 (2003)
18European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Pulsed Poloidal Current Drive (PPCD)
In RFX the PPCD experiments could be reproduced, although the performance increase was less pronounced.In particular, the core thermal diffusivity was reduced by a factor of 3.
R. Bartiromo et al., PRL 83, 1462 (1999)
PPCD
Standard
Standard
PPCD
19European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Oscillating poloidal current drive (OPCD)
OPCD is a periodic PPCD, obtained oscillating the current in the toroidal field coils. In RFX-mod it was shown that it periodically induces a QSH condition.
D. Terranova et al., PRL 99, 095001 (2007)
Dom
inan
t mod
e (%
)
Secondary modes (%)
QSH
MH
20European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Oscillating Field Current Drive
A current drive concept, in principle very efficient, has been proposed for obtaining a steady state RFP. Called Oscillating Field Current Drive (OFCD), or F- pumping, it is based on oscillating the toroidal and poloidal loop voltages (the latter by oscillating the current in the toroidal field coils) with proper phasing.
On ZT-40M, where the technique was originally proposed, the outcome was mixed: antidrive worked as expected, but no drive was observed, because of enhance plasma-wall interaction.
M.K. Bevir, et al., PF 28, 1826 (1985)K. Schoenberg et al., PF 31, 2287 (1988)
Helicity balance ( ):
In stationary conditions K should be constant.An additional source can be obtained by oscillating toroidal voltage Vt and toroidal flux with frequency . The resulting term is VtVpsin()/, which is maximum for = /2
21European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Oscillating Field Current Drive
In MST 10% of the total plasma current has been produced by OFCD.
The optimal phase difference between Vt and Vp has been found to be smaller than the theoretical /2 value.
Efficiency was the same as for steady induction (0.1 A/W).
K.J. McCollam et al., PRL 96, 035003 (2006)
22European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Transport mechanisms: magnetic topology
In standard RFPs dynamo is usually driven by many m = 1 modes.
The superposition of the mode islands causes a stochastization of the plasma core good confinement only in the outer region.
This is called Multiple Helicity (MH) condition
Poincaré plotIn r- plane
Chaotic core region
Reversal surface(m=0 resonance)
23European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Transport mechanisms: core
G. Fiksel et al., PPCF 38, A213 (1996)T.M. Biewer et al., PRL 91, 045004 (2003)
The particle and energy transport inside the reversal surface have been measured to be due to magnetic turbulence, related to the dynamo modes.The thermal conductivity in the plasma core is consistent with expectations from theory of transport in a stochastic magnetic field.
24European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Transport mechanisms: edge
Measurements of the edge particle flux induced by electrostatic turbulence in RFX have given values compatible with the total particle flux predicted by transport simulations.The energy flux driven by magnetic turbulence was found to be small, and the one driven by electrostatic turbulence accounts at most for 30% of the total. The nature of this flux is still unclear: better attention should be paid to magnetic topology and toroidal asymmetries.
V. Antoni et al., PRL 80, 4185 (1998)G. Serianni et al., PPCF 43, 919 (2001)E. Martines et al., NF 39, 581 (1999).
25European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Transport mechanisms: momentum transport
In RFX the perpendicular (toroidal) flow profile has been measured using the Gundestrup probe technique. The profile is consistent with the EB profile due to the radial electric field.The profile displays a double shear layer, one across the plasma boundary and the other more internal (confirmed by spectroscopic flow measurements).The electrostatic Reynolds stress in T2 and RFX displays a gradient on the shear layers, suggesting that the electrostatic turbulence is responsible for momentum transport. The magnetic Reynolds stress is found to be negligible.
V. Antoni, PRL 79, 4814 (1997)N. Vianello, PRL 94, 135001 (2005)
26European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
A good fit to the RFP confinement database is given by the constant scaling, also named Connor-Taylor scaling.
This would predict ohmic ignition at 10-20 MA of plasma current.
RFX was designed according to this scaling, which predicts E = 10 ms at 2 MA.
Scaling laws: The constant beta scaling
N = na2
All in SI units, Ip in MA, Ip/N in 10-14 Am
Notice that Ip/N = (n/ng)-1
Data from:K. A. Werley et al, NF 36, 629 (1996).
MST & RFX points are OLD!
2/3p
2/3pE
pp
2
)N/I(I
)N/I(IT.cst
B/nT
27European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Scaling laws: Improved confinement in MST
Recent results from MST (unpublished):
It is worth mentioning that these are values obtained in transient experiments.
28European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Scaling laws: Comparison MST-tokamak
J. Sarff et al., Nucl. Fusion 43, 1684 (2003).
Approach: compare to an H-mode
tokamak with:
• same size and input power
• Bt = 1 T
29European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
The shell problem: Need for a conducting shell
All RFP machines were built with a conducting shell around the vacuum vessel.
Motivations:
1. To control the horizontal plasma position (but can be done with vertical field coils)
2. To provide a flux conserver for toroidal field reversal (but not needed with aided reversal)
3. To provide a Br = 0 boundary condition for MHD instabilities (crucial !).
A conducting shell is however not feasible for a steady-state reactor.
30European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
The shell problem: Thin shell and RWM
The Culham team equipped the HBTX device with a thin shell (HBTX1C) having a time constant of 0.5 ms (shorter than the discharge duration).
The growth of non-resonant m=1 wall-locked MHD modes (Resistive Wall Modes) on a time constant of the order of the shell constant was observed, leading to premature discharge termination.
B. Alper et al., PPCF 31, 205 (1989)
31European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
The shell problem: The RFX-mod virtual shell
During the 1999-2004 shutdown the RFX experiment has been equipped with a 50 ms shell (previously 400 ms) and a sophisticated system of 192 feedback-controlled saddle coils covering the whole torus surface.
The new system led to enhanced performance (500 ms discharges), RWM suppression and mitigation of tearing mode amplitude and locking phenomena.
L. Marrelli et al., PPCF 49, B359 (2007)
no MHD activecontrol
with MHD active control: 2006
upgraded MHD active control: june 2007
32European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
The shell problem: RWM control in RFX-mod
See also T. Bolzonella’s lesson tomorrow.
In particular, the system of feedback-controlled saddle coils has been shown to be able to completely suppress the Resistive Wall Modes, thus eliminating the need of a shell with long time constant.
Future RFPs will only need a thin shell (possibly the vessel itself), for the fast time scales.
plasma current
m=1,n=-6 mode amplitude
t [s]
logarithmic mode amplitude
mode control
mode controlmode control
33European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Mode locking: The RFX experience
In RFX, since the early operations, the dynamo m=1 tearing modes locked routinely yielding:• Phase locking: all modes superpose coherently at one toroidal angle, giving rise to a localized magnetic perturbation.• Wall locking: the localized perturbation is stationary, and causes a strong interaction in one limited area of the first wall.These phenomena limited for many years the achievable plasma current to 1 MA.
P. Zanca et al, PP 8, 516 (2001)
34European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Mode locking: The RFX experience
m=1 m=0
The m=0 modes (low n) also lock in phase, superposing their nodes, giving rise to a funnel-like shape of the plasma column.
Overall, a local shift of 2-3 cm was measured, giving rise to strong plasma-wall interaction.
P. Zanca et al, PP 8, 516 (2001)
35European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Mode locking: The MST experience
In MST the m=1 dynamo modes are typically found to rotate at frequencies ~ 10 kHz.Occasionally, the modes slow down and lock to the wall, while the plasma continues to rotate at reduced speed. This happens especially in QSH states.Mode locking does not lead to disruptions, as is the case for tokamaks.
B.E. Chapman et al., PP 11, 2156 (2004).
Often, the modes afterwards unlock spontaneously.
36European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Mode locking: rotation by m=0 perturbation
In RFX a rotation the localized magnetic perturbation could be unlocked by applying an m=0 rotating perturbation using the toroidal field coils.The non-linear coupling between m=0 and m=1 modes is exploited.
R. Bartiromo et al., PRL 83, 1779 (1999)
37European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
#22805 Clean Mode Control#18942 Intelligent Shell
Mode locking: unlocking by active control
tm ,1 Plasma surface distortion
In RFX-mod the wall locking is removed by the feedback-controlled saddle coil system, since the so-called “Clean Mode Control” (with sideband removal from the measurements) has been implemented.
P. Zanca et al., NF 47, 1825 (2007)
38European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Mode locking: unlocking by active control
Mode rotation can be made more reproducible by slightly modifying the feedback algorithm,i.e. by setting a non-zero reference value for selected helicities (in this case the m=1/n=7 mode).
L. Marrelli et al., PPCF 49, B359 (2007).
Mod
e am
plitu
des
n=7
phas
e (d
eg)
39European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: Multiple Helicity
In low current RFPs dynamo is usually driven by many m = 1 modes.
The superposition of the mode islands causes a stochastization of the plasma core good confinement only in the outer region.
This is called Multiple Helicity (MH) condition
Poincaré plotIn r- plane
Chaotic core region
40European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
In principle, it is possible to have the B reversal with one mode only (laminar dynamo). This is called Single Helicity (SH) state.
3D MHD simulations have shown the spontaneous transition from a MH state to a SH state when the Hartmann number is varied.
In SH, good magnetic surfaces are recovered good confinement over the whole plasma.
Advanced RFP: From MH to SH (theory)
S. Cappello et al., PRL 85, 3838 (2000)
2/1H
41European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: From MH to (Q)SH (experiment)
Quasi Single Helicity (QSH) states, where the most internally resonant mode (n = 7 for RFX-mod) dominates, and the secondary mode amplitudes are reduced, are routinely observed.
A typical feature is the appearance of a hot magnetic island.
(m=1, n=-7)
q, s
afet
y fa
ctor
r/a
(1, -8)(1, -9)
(1, -10)
Weak m=1 secondary modes
42European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: Dynamic behaviour of QSH
Spontaneous intermittent transition from QSH to MH and back.
More likely at high current. Feedback control of edge Br is essential!
Ip
(MA)
time (s)
m=1,n=-7 <m=1,n=-8 to -15>
b/B(a)(%)
> 10E
R
43European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: Scaling with Lundquist number
S = R / A =
Dominant mode (m = 1, n = -7) Secondary modes (1,-8 to -15)
bdom
bsecd
5%0.2%
= = 25
b/B
(%)
b/B
(%)
S S
Lundquist number:
44European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: Scaling with plasma current
Since S grows with Ip and Te, we have an encouraging scaling with Ip: the dominant mode saturates, the secondary modes keep decreasing.
Dominant Secondary
45European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: Relative duration of QSH
The flat-top fraction spent in QSH state and the QSH duration increase with Lundquist number.
46European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: Single Helical Axis (SHAx) states
When the dominant mode amplitude exceeds a threshold, the main magnetic axis collapses onto the island X-point and the separatrix is expelled.
The island O-point remains as the magnetic axis of a helically distorted plasma.
We call this condition Single Helical Axis (SHAx) state, as opposed do QSH with island (QSHi).
SHAx states are predicted to be more resilient to chaos.
b/ B 2% b/ B 3% b/ B 4% b/ B 5%
R. Lorenzini et al., Phys. Rev. Lett. 101, 025005 (2008)
47European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: Evidence of transition to SHAx
QSHi
SHAx
Dominant mode amplitude (%)
The
rmal
str
uctu
re w
idth
(m
)
MH
SHAx
QSHi
Te
(ev)
r (m)
QSHi = QSH with island
The SHAx occurrence allows an enlargement of the hot region to the other side of the chamber geometrical axis, thus inducing an increase of the plasma thermal content.
48European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: condition for SHAx occurrence
Br at resonance(reconstr.)
B at wall(measured)
Dom.
Sec.
Dom./Sec.
Dom.
Sec.
Dom./Sec.
SHAx states, as detected from Te profiles, appear only when the dominant mode exceeds a threshold (which corresponds to a threshold of the ratio secondary/dominant)
49European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: SHAx are more chaos-resilient
QSHiSHAx
Dominant mode only
All modes
Dominant mode only
All modes
50European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: Mapping of Te on helical flux
51European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: Mapping of soft X-ray
52European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: Mapping of interferometric data
Conclusions: Conserved helical magnetic surfaces exist in SHAx states. Spontaneous emergence of order from chaos
When a pellet enters the helical hot region, an asymmetry is seen also on the interferometry data.
53European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Advanced RFP: Improved confinement
After the separatrix disappearance the energy confinement time doubles larger thermal content reduced Ohmic input power
95%percentiles
SHAx b/B > 4%
QSHi b/B <4%
E (m
s)
secondary mode amplitude (%)
assumingTe = Ti
54European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Density limit
In RFX a density limit is found, identical to tokamak’s Greenwald limit: n (1020) < Ip(MA)/(a2).However, contrary to tokamaks, no sudden current collapse (disruption) is observed at limit.At high density a belt of enhanced radiation is observed in the region where the m=0 mode locking shrinks the plasma, with a corresponding density accumulation. This could give rise to a MARFE-like phenomenology.
M.E. Puiatti et al., IAEA Fusion Energy Conference, Geneva (2008)
55European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
RFX-mod: Tokamak and RFP in the same device
RFX-mod has the unique feature of being able to produce both in RFP and tokamak plasma.
RFP
Tokamak
56European Doctorate in Fusion Science and Engineering - Garching, 29 September 2008
Where do we go from here?
The tendency of the plasma to move towards a QSH state when it becomes hotter, and the associated emergence of order in the chaotic core, opens up new perspectives for the RFP configuration.
The observation of a steady SHAx state is expected in RFX-mod at the design current of 2 MA (in 2009).
The following issues require priority attention (personal opinion):– Current drive (OFCD?)
– Plasma-wall interaction handling (helical limiter or divertor)
– Scaling laws (taking into account order emergence in SHAx states)
The outcome of this work could make a case for a new generation of multi-MA helical RFP devices.
It is an exciting time for being involved in RFP research !