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Experimental RFP results. Emilio Martines Consorzio RFX, Padova, Italy email: A bit of history Magnetic configuration Discharge formation Dynamo PPCD-OPCD Oscillating Field Current Drive (OFCD) Transport mechanisms Scaling laws. Density limit

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Experimental RFP results

Emilio Martines

Consorzio RFX, Padova, Italy


A bit of history

Magnetic configuration

Discharge formation



Oscillating Field Current Drive (OFCD)

Transport mechanisms

Scaling laws

Density limit

The shell problem

Mode locking

Advanced RFP: the Single Helicity paradigm

a bit of history zeta
A bit of history: ZETA

“Pinch device”. Operational from 1954 to 1968.

R = 1.5 m, a = 0.5 m, Ip = 800 kA.

Quiescent phase

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).

a bit of history 40 years of rfp research
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)

a bit of history 40 years of rfp research1
A bit of history: 40 years of RFP research

Padova (Italy)

Culham (UK)

Los Alamos (USA)

Tsukuba (Japan)

Nagoya (Japan)

San Diego (USA)

Tokyo/Kyoto (Japan)

Stockholm (Sweden)

Chengdu (China)

Madison (USA)

1st gen. (‘70s)




TPE-1R, R(M)







2nd gen. (‘80s)



ZT-40, ZT-40M








3rd gen. (‘90s)

RFX, RFX-mod


ZTH (canceled)








In red the experiments presently in operation. In bold the two “flagship” devices.

rfp devices presently in operation
RFP devices presently in operation









magnetic configuration what is a rfp
Magnetic configuration: What is a RFP?

In short: the RFP is an overdriven tokamak where the edge toroidal field is allowed to reverse.

RFX-mod has the unique feature of being able to produce both RFP and tokamak plasmas.

magnetic configuration f plot
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.

H.A.B. Bodin, A.A. Newton,

NF 20, 1255 (1980)

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.

magnetic configuration f plot1
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.

Ip (MA)

t (s)


magnetic configuration rfp profiles
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)

magnetic configuration rfp profiles1
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)

discharge formation self and aided reversal
Discharge formation: Self and aided reversal

The first RFP plasmas were obtained by “self-reversal”, that is exploiting the presence of a toroidal flux conserver (the toroidal field winding).

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.


aided reversal


shots 23287, 20276

discharge formation different start up scenarios
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 Ramped

15962 Matched

15938 Aided

discharge formation different start up scenarios1
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).

dynamo basic concept
Dynamo: Basic concept

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.

m = 1 MHD modes

dynamo measurement of the dynamo field
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 is 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)

pulsed poloidal current drive ppcd
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)

pulsed poloidal current drive ppcd1
Pulsed Poloidal Current Drive (PPCD)

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)



Equilibrium reconstruction with many constraints, including Faraday rotation, motional Stark effect, Thomson scattering and interferometry.

pulsed poloidal current drive ppcd2
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)

pulsed poloidal current drive ppcd3





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)

oscillating poloidal current drive opcd
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)


Dominant mode (%)


Secondary modes (%)

oscillating field current drive
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 enhanced plasma-wall interaction.

M.K. Bevir, et al., PoF 28, 1826 (1985)

K. Schoenberg et al., PoF 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

oscillating field current drive1
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)

transport mechanisms magnetic topology
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

Reversal surface

(m=0 resonance)

Poincaré plot

In r- plane

Chaotic core region

transport mechanisms core
Transport mechanisms: core

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.

G. Fiksel et al., PPCF 38, A213 (1996)

T.M. Biewer et al., PRL 91, 045004 (2003)

transport mechanisms edge
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).

transport mechanisms momentum transport
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 EB 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)

scaling laws the constant beta scaling
Scaling laws: The constant beta scaling

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.

Data from:

K. A. Werley et al, NF 36, 629 (1996).

MST & RFX points are OLD!

N = na2

All in SI units, Ip in MA, Ip/N in 10-14 Am

Notice that Ip/N = (n/ng)-1

scaling laws improved confinement in mst
Scaling laws: Improved confinement in MST

Recent results from MST (unpublished):

It is worth mentioning that these are values obtained in transient experiments.

density limit
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)

the shell problem need for a conducting shell
The shell problem: Need for a conducting shell
  • All RFP machines were built with a conducting shell around the vacuum vessel.
  • Motivations:
  • Control the horizontal plasma position (but can be done with vertical field coils)
  • Provide a Br = 0 boundary condition for MHD instabilities (crucial !).
  • Some people claim that the shell acts as a flux conserver during the discharge formation, but this is actually not the case.
  • A conducting shell is however not feasible for a steady-state reactor.
the shell problem thin shell and rwm
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)

the shell problem the rfx mod virtual shell
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.

upgraded MHD active

control: june 2007

with MHD active control: 2006

no MHD active


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)

the shell problem rwm control in rfx mod

plasma current

mode control

m=1,n=-6 mode amplitude

logarithmic mode amplitude

t [s]

mode control

mode control

The shell problem: RWM control in RFX-mod

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.

See also T. Bolzonella’s lesson this morning.

mode locking the rfx experience
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, PoP 8, 516 (2001)

mode locking the rfx experience1
Mode locking: The RFX experience

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, PoP 8, 516 (2001)



mode locking the mst experience
Mode locking: The MST experience

In MST the m=1 dynamo modes typically found 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., PoP 11, 2156 (2004).

Often, the modes afterwards unlock spontaneously.

mode locking rotation by m 0 perturbation
Mode locking: rotation by m=0 perturbation

In RFX 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)

mode locking unlocking by active control

#22805 Clean Mode Control

#18942 Intelligent Shell

Mode locking: unlocking by active control

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)

Plasma surface distortion

mode locking unlocking by active control1
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).

Mode amplitudes

n=7 phase (deg)

advanced rfp multiple helicity
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 plot

In r- plane

Chaotic core region

advanced rfp from mh to sh theory
Advanced RFP: From MH to SH (theory)

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.

S. Cappello et al., PRL 85, 3838 (2000)

advanced rfp from mh to q sh experiment

(m=1, n=-7)

(1, -8)

(1, -9)

(1, -10)

q, safety factor




Advanced RFP: From MH to (Q)SH (experiment)

Quasi Single Helicity (QSH) states, where the most internally resonant m = 1 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.

Weak m=1 secondary modes

advanced rfp dynamic behaviour of qsh




<m=1,n=-8 to -15>



> 10tE  tR

time (s)

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!
advanced rfp scaling with lundquist number

S = tR / tA =






= 25

Advanced RFP: Scaling with Lundquist number

Lundquist number:

Dominant mode (m = 1, n = -7)

Secondary modes (1,-8 to -15)

b/B (%)

b/B (%)



advanced rfp scaling with plasma current
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.



advanced rfp relative duration of qsh
Advanced RFP: Relative duration of QSH

The flat-top fraction spent in QSH state and the QSH duration increase with Lundquist number.

time spent in QSH state

PERSISTENCE = ----------------------------------

flat-top duration

advanced rfp single helical axis shax states

bf / B  2%

bf / B  3%

bf / B  4%

bf / B  5%

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). Both are flavors of the general QSH condition.
  • SHAx states are predicted to be more resilient to chaos.

R. Lorenzini et al., Phys. Rev. Lett. 101, 025005 (2008)

advanced rfp single helical axis shax states1



single O-point


2nd O-point

1st O-point

Advanced RFP: Single Helical Axis (SHAx) states
advanced rfp evidence of transition to shax




Te (ev)

Thermal structure width (m)



r (m)

Dominant mode amplitude (%)

Advanced RFP: Evidence of transition to SHAx

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.

QSHi= QSH with island

advanced rfp condition for shax occurrence







Advanced RFP: condition for SHAx occurrence

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)

Br at resonance


B at wall


advanced rfp shax are more chaos resilient
Advanced RFP: SHAx are more chaos-resilient


mode only


mode only



All modes

All modes

advanced rfp improved confinement
Advanced RFP: Improved confinement

The energy confinement in SHAx states:

  • x 2 with respect to QSH with island;
  • x 4 with respect to MH states.

Even better performance is obtained transiently with pellet injection.

High density not reached yet, due to problems in density control and fuelling.

assuming Te = Ti

Transiently achieved with pellets

tE (ms)



secondary mode amplitude (%)

 decreasing chaos

advanced rfp mapping of t e on helical flux
Advanced RFP: Mapping of Te on helical flux

An approximate equilibrium reconstruction based on the dominant mode eigenfunction computed through Newcomb’s equation has been developd.

The flux surfaces are found as contours of the helical flux .

The SHAx temperature profiles, asymmetric with respect to the geometrical axis, collapse onto a single profile when plotted as a function of =(/)1/2.

Te vs 

Te vs R

Te contours

advanced rfp mapping of soft x ray
Advanced RFP: Mapping of soft X-ray

The soft X-ray emission measured by a 78-chord tomographic system is easily fitted by a simple emissivity 3-parameter function of the helical flux, of the form

advanced rfp mapping of interferometric data
Advanced RFP: Mapping of interferometric data

When a pellet enters the helical hot region, an asymmetry is seen also on the interferometry data.

Again, the data from the interferometer are well fitted by a simple function of the helical flux.

Conclusions: Conserved helical magnetic surfaces exist in SHAx states.

Spontaneous emergence of order from chaos

advanced rfp a new start
Advanced RFP: A new start?

The results of the last three slides were published in the August 2009 issue of Nature Physics.

The conclusion of the paper stated:

This new vision supports a reappraisal of the RFP as a low-external-field, non-disruptive, ohmically heated approach to magnetic fusion, exploiting both self-organization and technological simplicity.

R. Lorenzini, E. Martines, P. Piovesan, D. Terranova, P. Zanca, M. Zuin, et al.,

Nature Physics 5, 570 (2009)

where do we go from here
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 (hopefully in 2010).
  • The following issues require priority attention (personal opinion):
    • Current drive (OFCD?). Also, serious evaluation of pulsed reactor concept.
    • Density control and plasma-wall interaction handling (helical limiter or divertor).
    • Scaling laws (taking into account order emergence in SHAx states).
    • Development of predictive helical solutions of MHD equations.
  • 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 !