Plasma stability
Encyclopedia
An important field of plasma physics is the stability of the plasma
. It usually only makes sense to analyze the stability of a plasma once it has been established that the plasma is in equilibrium
. "Equilibrium" asks whether there are net forces that will accelerate any part of the plasma. If there are not, then "stability" asks whether a small perturbation will grow, oscillate, or be damped out.
In many cases a plasma can be treated as a fluid and its stability analyzed with magnetohydrodynamics
(MHD). MHD theory is the simplest representation of a plasma, so MHD stability is a necessity for stable devices to be used for nuclear fusion
, specifically magnetic fusion energy. There are, however, other types of instabilities
, such as velocity-space instabilities in magnetic mirror
s and systems with beams. There are also rare cases of systems, e.g. the Field-Reversed Configuration
, predicted by MHD to be unstable, but which are observed to be stable, probably due to kinetic effects.
Plasma instabilities are also categorised into different modes:
Source: Andre Gsponer, "Physics of high-intensity high-energy particle beam propagation in open air and outer-space plasmas" (2004)
is a measure of plasma pressure normalized to the magnetic field
strength. (See magnetohydrodynamics
for a full definition.) MHD stability at high beta is crucial for a compact, cost-effective magnetic fusion reactor. Fusion power density varies roughly as β2 at constant magnetic field, or as βN4 at constant bootstrap fraction in configurations with externally driven plasma current. (Here βN = β /(I/aB) is the normalized beta.) In many cases MHD stability represents the primary limitation on beta and thus on fusion power density. MHD stability is also closely tied to issues of creation and sustainment of certain magnetic configurations, energy confinement, and steady-state operation. Critical issues include understanding and extending the stability limits through the use of a
variety of plasma configurations, and developing active means for reliable operation near those limits. Accurate predictive capabilities are needed, which will require the addition of new physics to existing MHD models. Although a wide range of magnetic configurations exist, the underlying MHD physics is common to all. Understanding of MHD stability gained in one configuration can benefit others, by verifying analytic theories, providing benchmarks for predictive MHD stability codes, and advancing the development of active control techniques.
The most fundamental and critical stability issue for magnetic fusion is simply that MHD instabilities often limit performance at high beta. In most cases the important instabilities are long wavelength, global modes, because of their ability to cause severe degradation of energy confinement or termination of the plasma. Some important examples that are common to many magnetic configurations are ideal kink modes, resistive wall modes, and neoclassical tearing modes. A possible consequence of violating stability boundaries is a disruption, a sudden loss of thermal energy often followed by termination of the discharge. The key issue thus includes understanding the nature of the beta limit in the various configurations, including the associated thermal and magnetic stresses, and finding ways to avoid the limits or mitigate the consequences. A wide range of approaches to preventing such instabilities is under investigation, including optimization of the configuration of the plasma and its confinement device, control of the internal structure of the plasma, and active control of the MHD instabilities.
the ultimate operational limit for most configurations. The long-wavelength kink mode and short-wavelength
ballooning mode limits are generally well understood and can in principle be avoided.
Intermediate-wavelength modes (n ~ 5–10 modes encountered in tokamak
edge plasmas, for
example) are less well understood due to the computationally intensive nature of the stability
calculations. The extensive beta limit database for tokamaks is consistent with ideal MHD stability limits, yielding agreement to within about 10% in beta for cases where the internal profiles of the
plasma are accurately measured. This good agreement provides confidence in ideal stability
calculations for other configurations and in the design of prototype fusion reactors.
, stellarator
, and other configurations, but a nearby conducting wall can significantly improve ideal kink mode stability in most configurations, including the tokamak, ST, reversed field pinch
(RFP), spheromak
, and possibly the FRC. In the advanced tokamak and ST, wall stabilization is critical for operation with a large bootstrap fraction. The spheromak requires wall stabilization to avoid the low-m,n tilt and shift modes, and possibly bending modes. However, in the presence of a non-ideal wall, the slowly growing RWM is unstable. The resistive wall mode has been a long-standing issue for the RFP, and has more recently been observed in tokamak experiments. Progress in understanding the physics of the RWM and developing the means to stabilize it could be directly applicable to all magnetic configurations. A closely related issue is to understand plasma rotation, its sources and sinks, and its role in stabilizing the RWM.
. The neoclassical tearing mode (NTM) is a metastable mode; in certain plasma configurations, a sufficiently large deformation of the bootstrap current produced by a “seed island” can contribute to the growth of the island. The NTM is already an important performance-limiting factor in many tokamak experiments, leading to degraded confinement or disruption. Although the basic mechanism is well established, the capability to predict the onset in present and future devices requires better understanding of the damping mechanisms which determine the threshold island size, and of the mode coupling by which other instabilities (such as sawteeth in tokamaks) can generate seed islands. Resistive Ballooning Mode
, similar to ideal ballooning, but with finite resistivity taken into consideration, provides another example of a resistive instability.
opportunity to improve MHD stability in a robust way. The benefits of discharge shaping and low
aspect ratio for ideal MHD stability have been clearly demonstrated in tokamaks and STs, and will
continue to be investigated in experiments such as DIII-D, Alcator C-Mod
, NSTX
, and MAST
. New
stellarator experiments such as NCSX
(proposed) will test the prediction that addition of
appropriately designed helical coils can stabilize ideal kink modes at high beta, and lower-beta tests
of ballooning stability are possible in HSX. The new ST experiments provide an opportunity to
test predictions that a low aspect ratio yields improved stability to tearing modes, including
neoclassical, through a large stabilizing “Glasser effect
” term associated with a large Pfirsch-Schlüter
current. Neoclassical tearing modes can be avoided by minimizing the bootstrap current in
quasi-helical and quasi-omnigenous stellarator configurations. Neoclassical tearing modes are also
stabilized with the appropriate relative signs of the bootstrap current and the magnetic shear; this
prediction is supported by the absence of NTMs in central negative shear regions of tokamaks.
Stellarator configurations such as the proposed NCSX, a quasi-axisymmetric stellarator design,
can be created with negative magnetic shear and positive bootstrap current to achieve stability to the
NTM. Kink mode stabilization by a resistive wall has been demonstrated in RFPs and tokamaks,
and will be investigated in other configurations including STs (NSTX) and spheromaks (SSPX).
A new proposal to stabilize resistive wall modes by a flowing liquid lithium wall needs further
evaluation.
avoidance of MHD instabilities. Maintaining the proper current density profile, for example, can
help to maintain stability to tearing modes. Open-loop optimization of the pressure and current
density profiles with external heating and current drive sources is routinely used in many devices.
Improved diagnostic measurements along with localized heating and current drive sources, now
becoming available, will allow active feedback control of the internal profiles in the near future.
Such work is beginning or planned in most of the large tokamaks (JET
, JT–60U
, DIII–D,
C–Mod
, and ASDEX–U
) using RF
heating and current drive. Real-time analysis of profile data
such as MSE current profile measurements and real-time identification of stability boundaries are
essential components of profile control. Strong plasma rotation can stabilize resistive wall modes,
as demonstrated in tokamak experiments, and rotational shear is also predicted to stabilize resistive
modes. Opportunities to test these predictions are provided by configurations such as the ST,
spheromak, and FRC, which have a large natural diamagnetic rotation, as well as tokamaks with
rotation driven by neutral beam injection. The Electric Tokamak
experiment is intended to have a
very large driven rotation, approaching Alfvénic
regimes where ideal stability may also be
influenced. Maintaining sufficient plasma rotation, and the possible role of the RWM in damping
the rotation, are important issues that can be investigated in these experiments.
beyond the “passive” stability limits. Localized rf current drive at the rational surface is predicted
to reduce or eliminate neoclassical tearing mode islands. Experiments have begun in ASDEX–U
and COMPASS-D with promising results, and are planned for next year in DIII–D. Routine use
of such a technique in generalized plasma conditions will require real-time identification of the
unstable mode and its radial location. If the plasma rotation needed to stabilize the resistive wall
mode cannot be maintained, feedback stabilization with external coils will be required. Feedback
experiments have begun in DIII–D and HBT-EP, and feedback control should be explored for the
RFP and other configurations. Physics understanding of these active control techniques will be
directly applicable between configurations.
principal means of avoiding disruptions. However, in the event that these techniques do not
prevent an instability, the effects of a disruption can be mitigated by various techniques.
Experiments in
JT–60U have demonstrated reduction of electromagnetic stresses through operation at a neutral
point for vertical stability. Pre-emptive removal of the plasma energy by injection of a large gas
puff or an impurity pellet has been demonstrated in tokamak experiments, and ongoing
experiments in C–Mod, JT–60U, ASDEX–U, and DIII–D will improve the understanding and
predictive capability. Cryogenic liquid jets of helium are another proposed technique, which may
be required for larger devices. Mitigation techniques developed for tokamaks will be directly
applicable to other configurations.
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
. It usually only makes sense to analyze the stability of a plasma once it has been established that the plasma is in equilibrium
Mechanical equilibrium
A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....
. "Equilibrium" asks whether there are net forces that will accelerate any part of the plasma. If there are not, then "stability" asks whether a small perturbation will grow, oscillate, or be damped out.
In many cases a plasma can be treated as a fluid and its stability analyzed with magnetohydrodynamics
Magnetohydrodynamics
Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...
(MHD). MHD theory is the simplest representation of a plasma, so MHD stability is a necessity for stable devices to be used for nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
, specifically magnetic fusion energy. There are, however, other types of instabilities
Instability
In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds...
, such as velocity-space instabilities in magnetic mirror
Magnetic mirror
A magnetic mirror is a magnetic field configuration where the field strength changes when moving along a field line. The mirror effect results in a tendency for charged particles to bounce back from the high field region....
s and systems with beams. There are also rare cases of systems, e.g. the Field-Reversed Configuration
Field-Reversed Configuration
A Field-Reversed Configuration is a device developed for magnetic fusion energy research that confines a plasma on closed magnetic field lines without a central penetration....
, predicted by MHD to be unstable, but which are observed to be stable, probably due to kinetic effects.
Plasma instabilities
Plasma instabilities can be divided into two general groups:- hydrodynamic instabilities
- kinetic instabilities.
Plasma instabilities are also categorised into different modes:
| Mode (azimuthal wave number) | Note | Description | Radial modes | Description |
| m=0 | Sausage instability: displays harmonic variations of beam radius with distance along the beam axis | n=0 | Axial hollowing | |
| n=1 | Standard sausaging | |||
| n=2 | Axial bunching | |||
| m=1 | Sinuous, kink or hose instability: represents transverse displacements of the beam cross-section without change in the form or in a beam characteristics other than the position of its center of mass | |||
| m=2 | Filamentation modes: growth leads towards the breakup of the beam into separate filaments. | Gives an elliptic cross-section | ||
| m=3 | Gives a pyriform (pear-shaped) cross-section | |||
Source: Andre Gsponer, "Physics of high-intensity high-energy particle beam propagation in open air and outer-space plasmas" (2004)
List of plasma instabilities
|
|
MHD Instabilities
BetaBeta (plasma physics)
The beta of a plasma, symbolized by β, is the ratio of the plasma pressure to the magnetic pressure...
is a measure of plasma pressure normalized to the magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
strength. (See magnetohydrodynamics
Magnetohydrodynamics
Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...
for a full definition.) MHD stability at high beta is crucial for a compact, cost-effective magnetic fusion reactor. Fusion power density varies roughly as β2 at constant magnetic field, or as βN4 at constant bootstrap fraction in configurations with externally driven plasma current. (Here βN = β /(I/aB) is the normalized beta.) In many cases MHD stability represents the primary limitation on beta and thus on fusion power density. MHD stability is also closely tied to issues of creation and sustainment of certain magnetic configurations, energy confinement, and steady-state operation. Critical issues include understanding and extending the stability limits through the use of a
variety of plasma configurations, and developing active means for reliable operation near those limits. Accurate predictive capabilities are needed, which will require the addition of new physics to existing MHD models. Although a wide range of magnetic configurations exist, the underlying MHD physics is common to all. Understanding of MHD stability gained in one configuration can benefit others, by verifying analytic theories, providing benchmarks for predictive MHD stability codes, and advancing the development of active control techniques.
The most fundamental and critical stability issue for magnetic fusion is simply that MHD instabilities often limit performance at high beta. In most cases the important instabilities are long wavelength, global modes, because of their ability to cause severe degradation of energy confinement or termination of the plasma. Some important examples that are common to many magnetic configurations are ideal kink modes, resistive wall modes, and neoclassical tearing modes. A possible consequence of violating stability boundaries is a disruption, a sudden loss of thermal energy often followed by termination of the discharge. The key issue thus includes understanding the nature of the beta limit in the various configurations, including the associated thermal and magnetic stresses, and finding ways to avoid the limits or mitigate the consequences. A wide range of approaches to preventing such instabilities is under investigation, including optimization of the configuration of the plasma and its confinement device, control of the internal structure of the plasma, and active control of the MHD instabilities.
Ideal Instabilities
Ideal MHD instabilities driven by current or pressure gradients representthe ultimate operational limit for most configurations. The long-wavelength kink mode and short-wavelength
ballooning mode limits are generally well understood and can in principle be avoided.
Intermediate-wavelength modes (n ~ 5–10 modes encountered in tokamak
Tokamak
A tokamak is a device using a magnetic field to confine a plasma in the shape of a torus . Achieving a stable plasma equilibrium requires magnetic field lines that move around the torus in a helical shape...
edge plasmas, for
example) are less well understood due to the computationally intensive nature of the stability
calculations. The extensive beta limit database for tokamaks is consistent with ideal MHD stability limits, yielding agreement to within about 10% in beta for cases where the internal profiles of the
plasma are accurately measured. This good agreement provides confidence in ideal stability
calculations for other configurations and in the design of prototype fusion reactors.
Resistive Wall Modes
Resistive wall modes (RWM) develop in plasmas that require the presence of a perfectly conducting wall for stability. RWM stability is a key issue for many magnetic configurations. Moderate beta values are possible without a nearby wall in the tokamakTokamak
A tokamak is a device using a magnetic field to confine a plasma in the shape of a torus . Achieving a stable plasma equilibrium requires magnetic field lines that move around the torus in a helical shape...
, stellarator
Stellarator
A stellarator is a device used to confine a hot plasma with magnetic fields in order to sustain a controlled nuclear fusion reaction. It is one of the earliest controlled fusion devices, first invented by Lyman Spitzer in 1950 and built the next year at what later became the Princeton Plasma...
, and other configurations, but a nearby conducting wall can significantly improve ideal kink mode stability in most configurations, including the tokamak, ST, reversed field pinch
Reversed field pinch
A reversed-field pinch is a device used to produce and contain near-thermonuclear plasmas. It is a toroidal pinch which uses a unique magnetic field configuration as a scheme to magnetically confine a plasma, primarily to study magnetic fusion energy. Its magnetic geometry is somewhat different...
(RFP), spheromak
Spheromak
A spheromak is an arrangement of plasma formed into a toroidal shape similar to a smoke ring. The spheromak contains large internal electrical currents and their associated magnetic fields arranged so the magnetohydrodynamic forces within the spheromak are nearly balanced, resulting in long-lived ...
, and possibly the FRC. In the advanced tokamak and ST, wall stabilization is critical for operation with a large bootstrap fraction. The spheromak requires wall stabilization to avoid the low-m,n tilt and shift modes, and possibly bending modes. However, in the presence of a non-ideal wall, the slowly growing RWM is unstable. The resistive wall mode has been a long-standing issue for the RFP, and has more recently been observed in tokamak experiments. Progress in understanding the physics of the RWM and developing the means to stabilize it could be directly applicable to all magnetic configurations. A closely related issue is to understand plasma rotation, its sources and sinks, and its role in stabilizing the RWM.
Resistive instabilities
Resistive instabilities are an issue for all magnetic configurations, since the onset can occur at beta values well below the ideal limit. The stability of neoclassical tearing modes (NTM) is a key issue for magnetic configurations with a strong bootstrap currentBootstrap current
In a toroidal fusion power device, a plasma is confined within a donut-shaped cylinder. If the gas pressure of the plasma varies across the radius of the cylinder, an electrical current will naturally arise within the plasma. This bootstrap current, and is commonly found in the tokamak reactor design...
. The neoclassical tearing mode (NTM) is a metastable mode; in certain plasma configurations, a sufficiently large deformation of the bootstrap current produced by a “seed island” can contribute to the growth of the island. The NTM is already an important performance-limiting factor in many tokamak experiments, leading to degraded confinement or disruption. Although the basic mechanism is well established, the capability to predict the onset in present and future devices requires better understanding of the damping mechanisms which determine the threshold island size, and of the mode coupling by which other instabilities (such as sawteeth in tokamaks) can generate seed islands. Resistive Ballooning Mode
Resistive ballooning mode
The resistive ballooning mode is an instability occurring in magnetized plasmas, particularly in magnetic confinement devices such as tokamaks, when the pressure gradient is opposite to the effective gravity created by a magnetic field....
, similar to ideal ballooning, but with finite resistivity taken into consideration, provides another example of a resistive instability.
Configuration
The configuration of the plasma and its confinement device represent anopportunity to improve MHD stability in a robust way. The benefits of discharge shaping and low
aspect ratio for ideal MHD stability have been clearly demonstrated in tokamaks and STs, and will
continue to be investigated in experiments such as DIII-D, Alcator C-Mod
Alcator C-Mod
Alcator C-Mod is a tokamak, a magnetically confined nuclear fusion device, at the MIT Plasma Science and Fusion Center. It is the tokamak with the highest magnetic field and highest plasma pressure in the world...
, NSTX
National Spherical Torus Experiment
The National Spherical Torus Experiment is an innovative magnetic fusion device based on the spherical tokamak concept that was constructed by the Princeton Plasma Physics Laboratory in collaboration with the Oak Ridge National Laboratory, Columbia University, and the University of Washington at...
, and MAST
Mega Ampere Spherical Tokamak
The Mega Ampere Spherical Tokamak, or MAST experiment is a nuclear fusion experiment in operation at Culham, Oxfordshire, England since December 1999. It follows the highly successful START experiment...
. New
stellarator experiments such as NCSX
National Compact Stellarator Experiment
The National Compact Stellarator Experiment is a plasma confinement experiment that was being conducted at the Princeton Plasma Physics Laboratory. NCSX used magnets and layout designed through massively parallel computing to find the optimal shape for the reactor vessel, leading to a compact device...
(proposed) will test the prediction that addition of
appropriately designed helical coils can stabilize ideal kink modes at high beta, and lower-beta tests
of ballooning stability are possible in HSX. The new ST experiments provide an opportunity to
test predictions that a low aspect ratio yields improved stability to tearing modes, including
neoclassical, through a large stabilizing “Glasser effect
Glasser effect
The Glasser effect describes the creation of singularities in the flow field of a magnetically confined plasma when small resonant preturbations modify the gradient of the pressure field.- External links :*...
” term associated with a large Pfirsch-Schlüter
current. Neoclassical tearing modes can be avoided by minimizing the bootstrap current in
quasi-helical and quasi-omnigenous stellarator configurations. Neoclassical tearing modes are also
stabilized with the appropriate relative signs of the bootstrap current and the magnetic shear; this
prediction is supported by the absence of NTMs in central negative shear regions of tokamaks.
Stellarator configurations such as the proposed NCSX, a quasi-axisymmetric stellarator design,
can be created with negative magnetic shear and positive bootstrap current to achieve stability to the
NTM. Kink mode stabilization by a resistive wall has been demonstrated in RFPs and tokamaks,
and will be investigated in other configurations including STs (NSTX) and spheromaks (SSPX).
A new proposal to stabilize resistive wall modes by a flowing liquid lithium wall needs further
evaluation.
Internal Structure
Control of the internal structure of the plasma allows more activeavoidance of MHD instabilities. Maintaining the proper current density profile, for example, can
help to maintain stability to tearing modes. Open-loop optimization of the pressure and current
density profiles with external heating and current drive sources is routinely used in many devices.
Improved diagnostic measurements along with localized heating and current drive sources, now
becoming available, will allow active feedback control of the internal profiles in the near future.
Such work is beginning or planned in most of the large tokamaks (JET
Joint European Torus
JET, the Joint European Torus, is the largest magnetic confinement plasma physics experiment worldwide currently in operation. Its main purpose is to open the way to future nuclear fusion experimental tokamak reactors such as ITER and :DEMO....
, JT–60U
JT-60
JT-60 is the flagship of Japan's magnetic fusion program, previously run by the Japan Atomic Energy Research Institute and currently run by the Japan Atomic Energy Agency's Naka Fusion Institute in Ibaraki Prefecture, Japan...
, DIII–D,
C–Mod
Alcator C-Mod
Alcator C-Mod is a tokamak, a magnetically confined nuclear fusion device, at the MIT Plasma Science and Fusion Center. It is the tokamak with the highest magnetic field and highest plasma pressure in the world...
, and ASDEX–U
ASDEX Upgrade
ASDEX Upgrade is a divertor tokamak, that went into operation at the Max-Planck-Institut für Plasmaphysik, Garching in 1991...
) using RF
Radio frequency
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
heating and current drive. Real-time analysis of profile data
such as MSE current profile measurements and real-time identification of stability boundaries are
essential components of profile control. Strong plasma rotation can stabilize resistive wall modes,
as demonstrated in tokamak experiments, and rotational shear is also predicted to stabilize resistive
modes. Opportunities to test these predictions are provided by configurations such as the ST,
spheromak, and FRC, which have a large natural diamagnetic rotation, as well as tokamaks with
rotation driven by neutral beam injection. The Electric Tokamak
Electric Tokamak
The UCLA Electric Tokamak is a low field magnetic fusion tokamak device with a large aspect ratio.The machine has a major radius of 5 metres, a minor radius of 1 metre, plasma current of 45 kiloamperes and can produce a core electron plasma temperature of 300 electronvolts. First plasma was...
experiment is intended to have a
very large driven rotation, approaching Alfvénic
Alfvén wave
An Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave.-Definition:An Alfvén wave in a plasma is a low-frequency travelling oscillation of the ions and the magnetic field...
regimes where ideal stability may also be
influenced. Maintaining sufficient plasma rotation, and the possible role of the RWM in damping
the rotation, are important issues that can be investigated in these experiments.
Feedback Control
Active feedback control of MHD instabilities should allow operationbeyond the “passive” stability limits. Localized rf current drive at the rational surface is predicted
to reduce or eliminate neoclassical tearing mode islands. Experiments have begun in ASDEX–U
and COMPASS-D with promising results, and are planned for next year in DIII–D. Routine use
of such a technique in generalized plasma conditions will require real-time identification of the
unstable mode and its radial location. If the plasma rotation needed to stabilize the resistive wall
mode cannot be maintained, feedback stabilization with external coils will be required. Feedback
experiments have begun in DIII–D and HBT-EP, and feedback control should be explored for the
RFP and other configurations. Physics understanding of these active control techniques will be
directly applicable between configurations.
Disruption Mitigation
The techniques discussed above for improving MHD stability are theprincipal means of avoiding disruptions. However, in the event that these techniques do not
prevent an instability, the effects of a disruption can be mitigated by various techniques.
Experiments in
JT–60U have demonstrated reduction of electromagnetic stresses through operation at a neutral
point for vertical stability. Pre-emptive removal of the plasma energy by injection of a large gas
puff or an impurity pellet has been demonstrated in tokamak experiments, and ongoing
experiments in C–Mod, JT–60U, ASDEX–U, and DIII–D will improve the understanding and
predictive capability. Cryogenic liquid jets of helium are another proposed technique, which may
be required for larger devices. Mitigation techniques developed for tokamaks will be directly
applicable to other configurations.