Spheromak
Encyclopedia
A spheromak is an arrangement of plasma
formed into a toroid
al shape similar to a smoke ring
. The spheromak contains large internal electrical currents and their associated magnetic field
s arranged so the magnetohydrodynamic forces within the spheromak are nearly balanced, resulting in long-lived (microsecond) confinement times without any external fields. Spheromak belongs to a type of plasma configuration referred to as the compact toroid
s.
The physics of the spheromak and their collisions is similar to a variety of astrophysical events, like coronal loop
s and filaments, relativistic jet
s and plasmoid
s. They are particularly useful for studying magnetic reconnection events, when two or more spheromaks collide. Spheromaks are easy to generate using a "gun" type device that ejects spheromaks off the end of an electrode into a holding area, called the flux conserver. This has made them useful in the laboratory setting, and spheromak guns are relatively common in astrophysics labs. These devices are often, confusingly, referred to simply as "spheromaks" as well; the term has two meanings.
Spheromaks have been proposed as a magnetic fusion energy concept due to their long confinement times, which was on the same order as the best tokamak
s when they were first being studied. Although they had some successes during the 1970s and 80s, these small and lower-energy devices had limited performance and most spheromak research ended when fusion funding was dramatically curtailed in the late 1980s. However, in the late 1990s important research demonstrated that hotter spheromaks have better confinement times, and this has led to a second wave of spheromak machines. Spheromaks have also been used as a mean of injecting plasma into a bigger magnetic confinement experiment like a tokamak
.
, a value
that describes the "twistedness" of the magnetic field in a plasma.
The earliest work on these concepts was developed by Hannes Alfvén
in 1943, work that won him the 1970 Nobel Prize in Physics
. His development of the concept of Alfvén wave
s explained the long-duration dynamics of plasma as electric current
s traveling within them produced magnetic field
s which, in a fashion similar to a dynamo
, gave rise to new currents. In 1950, Lundquist experimentally studied Alfvén waves in mercury
and introduced the characterizing Lundquist number
, which describes the conductivity of the plasma. In 1958, Woltjer, working on astrophysical plasmas, noted that the
value is conserved, which implies that a twisty field will attempt to maintain its twistyness even with external forces being applied to it.
Starting in 1959, Alfvén and a team including Lindberg, and Mitlid and Jacobsen built a device to create balls of plasma for study. This device was identical to modern "coaxial injector" devices (see below) and the experimenters were surprised to find a number of interesting behaviors. Among these was the creation of stable rings of plasma. In spite of their many successes, in 1964 the researchers turned to other areas and the injector concept lay dormant for two decades.
, Levine, and Waniek published a paper on the dynamics of large magnets, which demonstrated that the limiting factor in magnet performance was physical; stresses in the magnet would overcome its own mechanical limits. They proposed winding these magnets in such a way that the forces within the magnet windings cancelled out, the "force-free condition". Although it was not known at the time, this is the same magnetic field in a spheromak.
In 1957 the ZETA
machine started operation in the UK, it was at that time by far the largest and most powerful fusion device in the world. ZETA operated until 1968, by which point it was one of many devices of its size. During its operation, the experimental team noticed that on occasion the plasma would maintain its confinement long after the experimental run had ostensibly ended, although this was not studied in depth at that point. Years later in 1974, A.E. Taylor made great strides in characterizing these self-stable plasmas, which he called "quiescent". He developed the Taylor state
equilibrium concept, a state of plasma that conserves helicity in its lowest possible energy state. This led to a re-awakening of compact torus research.
In the aftermath of ZETA the "classical" z-pinch
concept fell from favour, and the newer theta-pinch saw a reduced level of activity. While working on such a machine in the early 1960s, one designed with a conical pinch area, Bostick and Wells found that the machine sometimes created stable rings of plasma. A series of machines to study the problem followed, and in one of these magnetic probe measurements found the toroidal magnetic field profile of a spheromak; the toroidal field was zero on axis, rose to a maximum at some interior point, and then went to zero at the wall. However, the theta-pinch failed to reach the high-energy conditions needed for fusion, and interest in the system waned. In spite of these tantalizing hints of interesting behaviour, most work on theta-pinch had ended by the 1970s.
, a combination of the plasma temperature, density and confinement time. Fusion devices generally fell into two classes, pulsed machines like the z-pinch
that attempted to reach high densities and temperatures but only for microseconds, while the steady state concepts like the stellarator
and magnetic mirror
attempted to reach the Lawson criterion through longer confinement times.
Taylor's work suggested that the self-stable plasmas would be a simple way to approach the problem along the confinement time axis. As Taylor's work became better known, it sparked off a new round of theoretical developments. In 1979 Rosenbluth and Bussac published a paper describing generalizations of Taylor's work, including a spherical minimum energy state having zero toroidal field on the bounding surface. This means that there is no externally driven current on the device axis and so there are no external toroidal field coils. It appeared that this approach would allow for fusion reactors of greatly simpler design than the existing stellarator
and tokamak
approaches.
Several experimental devices sprung up almost overnight. Wells, recognizing his earlier experiments as examples of these plasmas, was now at the University of Miami
and started gathering funding for a new device combining two of his earlier conical theta-pinch systems, which emerged as Trisops
. In Japan, Nihon University
built the PS-1, which used a combination of theta and zeta pinches to produce spheromaks. Harold Furth
was excited by the prospect of a less-expensive solution to the confinement issue, and started the S1 at the Princeton Plasma Physics Laboratory
, which used inductive heating. Many of these early experiments were summarized by Furth in 1983.
These early MFE experiments culminated in the Compact Torus Experiment (CTX) at Los Alamos
. This was the largest and most powerful spheromak device out there, generating spheromaks with surface currents of 1 MA, temperatures of 100 eV, and peak electron betas over 20%. CTX also experimented with methods to re-introduce energy into the fully formed spheromak in order to counter losses at the surface. In spite of these successes in the early stages of research, by the late 1980s the tokamak
device had surpassed the confinement times of the spheromaks by orders of magnitude; JET
was achieving confinement times on the orders of 30 seconds.
The major event that ended most spheromak work was not technical; funding for the entire US fusion program was dramatically curtailed in FY86, and many of the "alternate approaches", which includes spheromaks, were de-funded. Existing experiments in the US continued until their pre-arranged funding ran out, and the smaller programs elsewhere, notably in Japan and the new SPHEX machine in the UK, continued from 1979-1997. CTX gained some additional funding from the Defence Department and continued experiments until 1990; the last runs improved temperatures to 400 eV, and confinement times on the order of 3 ms.
community to understand a number of common events and the spheromak was studied as an add-on to existing MFE devices.
Hammer, Hartman et al. showed that spheromaks could be accelerated to extremely high velocities using a railgun
, and this led to several proposed uses. Among these was the use of such plasmas as "bullets" to fire at incoming warhead
s with the hope that the electrical currents would disrupt its electronics. This led to experiments on the Shiva Star
system, although these were cancelled in the mid-1990s. Other proposed uses included firing spheromaks at metal targets to generate intense X-ray
flashes as a backlighting source for other experiments.
In the late 1990s spheromak concepts were applied towards the study of fundamental plasma physics, notably magnetic reconnection
. Dual-spheromak machines were built at the University of Tokyo
, Princeton
(MRX) and Swarthmore College
. D.M. Rust and A. Kumar were particularly active in using spheromak-related concepts of magnetic helicity and relaxation to study solar prominences. Similar work was carried out at Caltech by Bellan and Hansen at Caltech, and the Swarthmore Spheromak Experiment (SSX) project at Swarthmore College
.
Some MFE work continued through this period, almost all of it using spheromaks as accessory devices for other reactors. Caltech and INRS-EMT
in Canada both used accelerated spheromaks as a way to refuel tokamaks. Others studied the use of spheromaks to inject helicity into tokamaks, eventually leading to the Helicity Injected Spherical Torus (HIST) device and similar concepts for a number of existing devices.
generally states that higher temperatures in a given confinement area will lead to higher density and pressure. In conventional devices like the tokamak this increased temperature/pressure gives rise to turbulence that dramatically lowers confinement time. If the spheromak really did give improved confinement with increased temperature, this would be enormously important. A series of similar papers followed, all of which suggested that there might be a "fast path" to an ignition-level spheromak reactor.
The promise was so great that several new MFE experiments have started to study these issues. Notable among these is the Sustained Spheromak Physics Experiment
(SSPX) at LLNL, which is studying the problems of generating long-life spheromaks through electrostatic injection of additional helicity. It remains unclear whether or not the spheromak can reach a suitable combination of confinement time and temperature to make a practical fusion reactor.
and therefore are stable against many instabilities. Typically, the current decays faster in the colder regions until the gradient in helicity is large enough to allow a turbulent redistribution of the current.
Force free vortices follow the following equations.
The first equation describes a Lorentz force
-free fluid: the
forces are everywhere zero. For a laboratory plasma α is a constant and β is a scalar function of spatial coordinates.
Note that, unlike most plasma structures, the Lorentz force
and the Magnus force
,
,
play equivalent roles.
is the mass density.
The magnetic flux surfaces in a spheromak are toroidal, with the current being totally toroidal
at the core of the torus and totally poloidal
at the surface of the torus. This is similar to the field configuration of a tokamak
, except that the field-producing coils are simpler and do not penetrate the plasma torus.
Spheromaks are subject to external forces, notably the thermal gradient between the hot plasma and its cooler surroundings. Generally this leads to a loss of energy at the outer surface of the spheromak though black body radiation, leading to a thermal gradient in the spheromak itself. Electrical current travels slower in the cooler sections, eventually leading to a redistribution of energy inside, and turbulence eventually destroys the spheromak.
The most common modern device is the "Marshall gun" or "injector". The device consists of two closed cylinders, one inside the other. The inner cylinder is shorter than the outer one, leaving an empty space at the bottom. An electromagnet inside the inner cylinder is used to set up an initial field; the field is similar to the one from a bar magnet, running vertically down the center of the inner cylinder and up again outside of the apparatus. The magnet is positioned so the area where it loops over from the center to outside, where the field lines are roughly horizontal, is aligned with the bottom of the inner cylinder.
To create a spheromak, a small puff of gas is introduced to the area between the cylinders. A large electric charge supplied by a capacitor
bank is applied across the cylinders, ionizing the gas. Currents induced into the resulting plasma interact with the original magnetic field, generating a Lorentz force
that pushes the plasma away from the inner cylinder, down into the empty area below. After a short period the plasma stabilizes into a spheromak.
Other common devices include open-ended or conical theta-pinch, where they were first researched in depth, and modern machines that generate them magnetically in a steady state.
Since the spheromak's magnetic confinement is self-generated, no external magnet coils are required. However, the spheromak does experience the "tilting perturbation" that allows it to rotate within the confinement area. This can be addressed with external magnets, but it is generally solved by wrapping the confinement area in a conductor, typically copper
. When the edge of the spheromak torus approaches the concudtive surface, a current is induced into it that, through Lens law, reacts to push the spheromak back into the center of the chamber.
It is also possible to get the same effect with a single conductor running down the center of the chamber, through the "hole" in the center of the spheromak. As this conductor's currents are self-generated, it adds little complexity to the design. However, stability can be further improved by running an external current in the central conductor. As the current scales up it approaches the conditions of a traditional tokamak, but in a much smaller size and simpler form. This evolution led to considerable research on the spherical tokamak
during the 1990s.
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...
formed into a toroid
Toroid
Toroid may refer to*Toroid , a doughnut-like solid whose surface is a torus.*Toroidal inductors and transformers which have wire windings on circular ring shaped magnetic cores.*Vortex ring, a toroidal flow in fluid mechanics....
al shape similar to a smoke ring
Smoke ring
A smoke ring is a visible vortex ring formed by sudden release of smoke. It can be created by blowing smoke from the mouth, quickly lighting a cigarette lighter and putting it out or holding a burning incense stick or a cigarette vertically, pushing it with the burning side up and suddenly pulling...
. The spheromak contains large internal electrical currents and their associated 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;...
s arranged so the magnetohydrodynamic forces within the spheromak are nearly balanced, resulting in long-lived (microsecond) confinement times without any external fields. Spheromak belongs to a type of plasma configuration referred to as the compact toroid
Compact toroid
Compact toroids are a class of toroidal plasma configurations that are self-stable, and whose configuration does not require magnet coils running through the center of the toroid. They are studied primarily in the field of fusion energy, where the lack of complex magnets and a simple geometry may...
s.
The physics of the spheromak and their collisions is similar to a variety of astrophysical events, like coronal loop
Coronal loop
Coronal loops form the basic structure of the lower corona and transition region of the Sun. These highly structured and elegant loops are a direct consequence of the twisted solar magnetic flux within the solar body. The population of coronal loops can be directly linked with the solar cycle; it...
s and filaments, relativistic jet
Relativistic jet
Relativistic jets are extremely powerful jets of plasma which emerge from presumed massive objects at the centers of some active galaxies, notably radio galaxies and quasars. Their lengths can reach several thousand or even hundreds of thousands of light years...
s and plasmoid
Plasmoid
A plasmoid is a coherent structure of plasma and magnetic fields. Plasmoids have been proposed to explain natural phenomena such as ball lightning, magnetic bubbles in the magnetosphere, and objects in cometary tails, in the solar wind, in the solar atmosphere, and in the heliospheric current sheet...
s. They are particularly useful for studying magnetic reconnection events, when two or more spheromaks collide. Spheromaks are easy to generate using a "gun" type device that ejects spheromaks off the end of an electrode into a holding area, called the flux conserver. This has made them useful in the laboratory setting, and spheromak guns are relatively common in astrophysics labs. These devices are often, confusingly, referred to simply as "spheromaks" as well; the term has two meanings.
Spheromaks have been proposed as a magnetic fusion energy concept due to their long confinement times, which was on the same order as the best 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...
s when they were first being studied. Although they had some successes during the 1970s and 80s, these small and lower-energy devices had limited performance and most spheromak research ended when fusion funding was dramatically curtailed in the late 1980s. However, in the late 1990s important research demonstrated that hotter spheromaks have better confinement times, and this has led to a second wave of spheromak machines. Spheromaks have also been used as a mean of injecting plasma into a bigger magnetic confinement experiment like a 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...
.
History
The spheromak has undergone several distinct periods of investigation, with the greatest efforts during the 1980s, and a reemergence in the 2000s.Background work in astrophysics
A key concept in the understanding of the spheromak is magnetic helicityMagnetic helicity
In plasma physics, magnetic helicity is the extent to which a magnetic field "wraps around itself". It is a generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field...
, a value
that describes the "twistedness" of the magnetic field in a plasma.The earliest work on these concepts was developed by Hannes Alfvén
Hannes Alfvén
Hannes Olof Gösta Alfvén was a Swedish electrical engineer, plasma physicist and winner of the 1970 Nobel Prize in Physics for his work on magnetohydrodynamics . He described the class of MHD waves now known as Alfvén waves...
in 1943, work that won him the 1970 Nobel Prize in Physics
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
. His development of the concept of Alfvén wave
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...
s explained the long-duration dynamics of plasma as electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
s traveling within them produced 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;...
s which, in a fashion similar to a dynamo
Dynamo
- Engineering :* Dynamo, a magnetic device originally used as an electric generator* Dynamo theory, a theory relating to magnetic fields of celestial bodies* Solar dynamo, the physical process that generates the Sun's magnetic field- Software :...
, gave rise to new currents. In 1950, Lundquist experimentally studied Alfvén waves in mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...
and introduced the characterizing Lundquist number
Lundquist number
In plasma physics, the Lundquist number is the dimensionless ratio of an Alfvén wave crossing timescale to a resistive diffusion timescale...
, which describes the conductivity of the plasma. In 1958, Woltjer, working on astrophysical plasmas, noted that the
value is conserved, which implies that a twisty field will attempt to maintain its twistyness even with external forces being applied to it.Starting in 1959, Alfvén and a team including Lindberg, and Mitlid and Jacobsen built a device to create balls of plasma for study. This device was identical to modern "coaxial injector" devices (see below) and the experimenters were surprised to find a number of interesting behaviors. Among these was the creation of stable rings of plasma. In spite of their many successes, in 1964 the researchers turned to other areas and the injector concept lay dormant for two decades.
Background work in fusion
In 1951 the first major efforts to produce controlled fusion with an aim to power production started in earnest. These early experiments generally used some sort of pulsed power in order to deliver the large magnetic forces required in the experiments, the magnitude of these currents and the forces that they produced were unprecedented. In 1957 Harold FurthHarold Furth
Harold P. Furth was an Austrian-American physicist.Furth emigrated to the United States in 1941. He graduated from Harvard University with a Bachelor's degree in 1951 and received his Ph.D. from Harvard in 1960...
, Levine, and Waniek published a paper on the dynamics of large magnets, which demonstrated that the limiting factor in magnet performance was physical; stresses in the magnet would overcome its own mechanical limits. They proposed winding these magnets in such a way that the forces within the magnet windings cancelled out, the "force-free condition". Although it was not known at the time, this is the same magnetic field in a spheromak.
In 1957 the ZETA
ZETA
ZETA, short for "Zero-Energy Toroidal Assembly", was a major experiment in the early history of fusion power research. It was the ultimate device in a series of UK designs using the Z-pinch confinement technique, and the first large-scale fusion machine to be built...
machine started operation in the UK, it was at that time by far the largest and most powerful fusion device in the world. ZETA operated until 1968, by which point it was one of many devices of its size. During its operation, the experimental team noticed that on occasion the plasma would maintain its confinement long after the experimental run had ostensibly ended, although this was not studied in depth at that point. Years later in 1974, A.E. Taylor made great strides in characterizing these self-stable plasmas, which he called "quiescent". He developed the Taylor state
Taylor state
In plasma physics, a Taylor state is the minimum energy state of a plasma satisfying the constraint of conserving magnetic helicity.- Derivation :...
equilibrium concept, a state of plasma that conserves helicity in its lowest possible energy state. This led to a re-awakening of compact torus research.
In the aftermath of ZETA the "classical" z-pinch
Z-pinch
In fusion power research, the Z-pinch, also known as zeta pinch or Bennett pinch , is a type of plasma confinement system that uses an electrical current in the plasma to generate a magnetic field that compresses it...
concept fell from favour, and the newer theta-pinch saw a reduced level of activity. While working on such a machine in the early 1960s, one designed with a conical pinch area, Bostick and Wells found that the machine sometimes created stable rings of plasma. A series of machines to study the problem followed, and in one of these magnetic probe measurements found the toroidal magnetic field profile of a spheromak; the toroidal field was zero on axis, rose to a maximum at some interior point, and then went to zero at the wall. However, the theta-pinch failed to reach the high-energy conditions needed for fusion, and interest in the system waned. In spite of these tantalizing hints of interesting behaviour, most work on theta-pinch had ended by the 1970s.
The golden age
The key concept in magnetic fusion energy (MFE) is the Lawson criterionLawson criterion
In nuclear fusion research, the Lawson criterion, first derived on fusion reactors by John D. Lawson in 1955 and published in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the...
, a combination of the plasma temperature, density and confinement time. Fusion devices generally fell into two classes, pulsed machines like the z-pinch
Z-pinch
In fusion power research, the Z-pinch, also known as zeta pinch or Bennett pinch , is a type of plasma confinement system that uses an electrical current in the plasma to generate a magnetic field that compresses it...
that attempted to reach high densities and temperatures but only for microseconds, while the steady state concepts like the 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 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....
attempted to reach the Lawson criterion through longer confinement times.
Taylor's work suggested that the self-stable plasmas would be a simple way to approach the problem along the confinement time axis. As Taylor's work became better known, it sparked off a new round of theoretical developments. In 1979 Rosenbluth and Bussac published a paper describing generalizations of Taylor's work, including a spherical minimum energy state having zero toroidal field on the bounding surface. This means that there is no externally driven current on the device axis and so there are no external toroidal field coils. It appeared that this approach would allow for fusion reactors of greatly simpler design than the existing 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 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...
approaches.
Several experimental devices sprung up almost overnight. Wells, recognizing his earlier experiments as examples of these plasmas, was now at the University of Miami
University of Miami
The University of Miami is a private, non-sectarian university founded in 1925 with its main campus in Coral Gables, Florida, a medical campus in Miami city proper at Civic Center, and an oceanographic research facility on Virginia Key., the university currently enrolls 15,629 students in 12...
and started gathering funding for a new device combining two of his earlier conical theta-pinch systems, which emerged as Trisops
Trisops
Trisops was an experimental machine for the study of magnetic confinement of plasmas with the ultimate goal of producing fusion power. The configuration was a variation of a compact toroid, a toroidal structure of plasma and magnetic fields with no coils penetrating the center...
. In Japan, Nihon University
Nihon University
Nihon University is the largest university in Japan. Akiyoshi Yamada, the minister of justice, founded Nihon Law School in October 1889....
built the PS-1, which used a combination of theta and zeta pinches to produce spheromaks. Harold Furth
Harold Furth
Harold P. Furth was an Austrian-American physicist.Furth emigrated to the United States in 1941. He graduated from Harvard University with a Bachelor's degree in 1951 and received his Ph.D. from Harvard in 1960...
was excited by the prospect of a less-expensive solution to the confinement issue, and started the S1 at the Princeton Plasma Physics Laboratory
Princeton Plasma Physics Laboratory
Princeton Plasma Physics Laboratory is a United States Department of Energy national laboratory for plasma physics and nuclear fusion science located on Princeton University's Forrestal Campus in Plainsboro Township, New Jersey. Its primary mission is research into and development of fusion as an...
, which used inductive heating. Many of these early experiments were summarized by Furth in 1983.
These early MFE experiments culminated in the Compact Torus Experiment (CTX) at Los Alamos
Los Alamos National Laboratory
Los Alamos National Laboratory is a United States Department of Energy national laboratory, managed and operated by Los Alamos National Security , located in Los Alamos, New Mexico...
. This was the largest and most powerful spheromak device out there, generating spheromaks with surface currents of 1 MA, temperatures of 100 eV, and peak electron betas over 20%. CTX also experimented with methods to re-introduce energy into the fully formed spheromak in order to counter losses at the surface. In spite of these successes in the early stages of research, by the late 1980s the 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...
device had surpassed the confinement times of the spheromaks by orders of magnitude; 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....
was achieving confinement times on the orders of 30 seconds.
The major event that ended most spheromak work was not technical; funding for the entire US fusion program was dramatically curtailed in FY86, and many of the "alternate approaches", which includes spheromaks, were de-funded. Existing experiments in the US continued until their pre-arranged funding ran out, and the smaller programs elsewhere, notably in Japan and the new SPHEX machine in the UK, continued from 1979-1997. CTX gained some additional funding from the Defence Department and continued experiments until 1990; the last runs improved temperatures to 400 eV, and confinement times on the order of 3 ms.
Spheromaks in the lab
The data and theory from these experiments did not go to waste; through the early 1990s their work was widely used in the astrophysicsAstrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
community to understand a number of common events and the spheromak was studied as an add-on to existing MFE devices.
Hammer, Hartman et al. showed that spheromaks could be accelerated to extremely high velocities using a railgun
Railgun
A railgun is an entirely electrical gun that accelerates a conductive projectile along a pair of metal rails using the same principles as the homopolar motor. Railguns use two sliding or rolling contacts that permit a large electric current to pass through the projectile. This current interacts...
, and this led to several proposed uses. Among these was the use of such plasmas as "bullets" to fire at incoming warhead
Warhead
The term warhead refers to the explosive material and detonator that is delivered by a missile, rocket, or torpedo.- Etymology :During the early development of naval torpedoes, they could be equipped with an inert payload that was intended for use during training, test firing and exercises. This...
s with the hope that the electrical currents would disrupt its electronics. This led to experiments on the Shiva Star
Shiva Star
Shiva Star, originally just SHIVA, is a high-powered pulsed-power research device located at the Air Force Research Laboratory on the Kirtland Air Force Base in Albuquerque, New Mexico...
system, although these were cancelled in the mid-1990s. Other proposed uses included firing spheromaks at metal targets to generate intense X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
flashes as a backlighting source for other experiments.
In the late 1990s spheromak concepts were applied towards the study of fundamental plasma physics, notably magnetic reconnection
Magnetic reconnection
Magnetic reconnection is a physical process in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration...
. Dual-spheromak machines were built at the University of Tokyo
University of Tokyo
, abbreviated as , is a major research university located in Tokyo, Japan. The University has 10 faculties with a total of around 30,000 students, 2,100 of whom are foreign. Its five campuses are in Hongō, Komaba, Kashiwa, Shirokane and Nakano. It is considered to be the most prestigious university...
, Princeton
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
(MRX) and Swarthmore College
Swarthmore College
Swarthmore College is a private, independent, liberal arts college in the United States with an enrollment of about 1,500 students. The college is located in the borough of Swarthmore, Pennsylvania, 11 miles southwest of Philadelphia....
. D.M. Rust and A. Kumar were particularly active in using spheromak-related concepts of magnetic helicity and relaxation to study solar prominences. Similar work was carried out at Caltech by Bellan and Hansen at Caltech, and the Swarthmore Spheromak Experiment (SSX) project at Swarthmore College
Swarthmore College
Swarthmore College is a private, independent, liberal arts college in the United States with an enrollment of about 1,500 students. The college is located in the borough of Swarthmore, Pennsylvania, 11 miles southwest of Philadelphia....
.
Some MFE work continued through this period, almost all of it using spheromaks as accessory devices for other reactors. Caltech and INRS-EMT
INRS-EMT
The Énergie, Matériaux et Télécommunications is part of the INRS research university in Quebec. The center has two separate locations: Montreal and Varennes...
in Canada both used accelerated spheromaks as a way to refuel tokamaks. Others studied the use of spheromaks to inject helicity into tokamaks, eventually leading to the Helicity Injected Spherical Torus (HIST) device and similar concepts for a number of existing devices.
Rebirth in MFE
Then, in 1994, fusion history repeated itself. T. Kenneth Fowler was summarizing the results from CTX's experimental runs in the 1980s when he noticed that the confinement time was proportional to the temperature of the plasma. This is unexpected; the ideal gas lawIdeal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...
generally states that higher temperatures in a given confinement area will lead to higher density and pressure. In conventional devices like the tokamak this increased temperature/pressure gives rise to turbulence that dramatically lowers confinement time. If the spheromak really did give improved confinement with increased temperature, this would be enormously important. A series of similar papers followed, all of which suggested that there might be a "fast path" to an ignition-level spheromak reactor.
The promise was so great that several new MFE experiments have started to study these issues. Notable among these is the Sustained Spheromak Physics Experiment
Sustained Spheromak Physics Experiment
The Sustained Spheromak Physics Experiment is a program at Lawrence Livermore National Laboratory in the United States to investigate spheromak plasma....
(SSPX) at LLNL, which is studying the problems of generating long-life spheromaks through electrostatic injection of additional helicity. It remains unclear whether or not the spheromak can reach a suitable combination of confinement time and temperature to make a practical fusion reactor.
Theory
Force free plasma vortices have uniform magnetic helicityMagnetic helicity
In plasma physics, magnetic helicity is the extent to which a magnetic field "wraps around itself". It is a generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field...
and therefore are stable against many instabilities. Typically, the current decays faster in the colder regions until the gradient in helicity is large enough to allow a turbulent redistribution of the current.
Force free vortices follow the following equations.
The first equation describes a Lorentz force
Lorentz force
In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...
-free fluid: the
forces are everywhere zero. For a laboratory plasma α is a constant and β is a scalar function of spatial coordinates.Note that, unlike most plasma structures, the Lorentz force
Lorentz force
In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...
and the Magnus force
Magnus effect
The Magnus effect is the phenomenon whereby a spinning object flying in a fluid creates a whirlpool of fluid around itself, and experiences a force perpendicular to the line of motion...
,
,play equivalent roles.
is the mass density.The magnetic flux surfaces in a spheromak are toroidal, with the current being totally toroidal
Toroidal and poloidal
The earliest use of these terms cited by the Oxford English Dictionary is by Walter M. Elsasser in the context of the generation of the Earth's magnetic field by currents in the core, with "toroidal" being parallel to lines of latitude and "poloidal" being in the direction of the magnetic field...
at the core of the torus and totally poloidal
Toroidal and poloidal
The earliest use of these terms cited by the Oxford English Dictionary is by Walter M. Elsasser in the context of the generation of the Earth's magnetic field by currents in the core, with "toroidal" being parallel to lines of latitude and "poloidal" being in the direction of the magnetic field...
at the surface of the torus. This is similar to the field configuration of a 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...
, except that the field-producing coils are simpler and do not penetrate the plasma torus.
Spheromaks are subject to external forces, notably the thermal gradient between the hot plasma and its cooler surroundings. Generally this leads to a loss of energy at the outer surface of the spheromak though black body radiation, leading to a thermal gradient in the spheromak itself. Electrical current travels slower in the cooler sections, eventually leading to a redistribution of energy inside, and turbulence eventually destroys the spheromak.
Creating spheromaks
Spheromaks can be generated in a number of ways, which would be expected as they form naturally under a variety of conditions. These devices are sometimes, confusingly, referred to as spheromaks as well.The most common modern device is the "Marshall gun" or "injector". The device consists of two closed cylinders, one inside the other. The inner cylinder is shorter than the outer one, leaving an empty space at the bottom. An electromagnet inside the inner cylinder is used to set up an initial field; the field is similar to the one from a bar magnet, running vertically down the center of the inner cylinder and up again outside of the apparatus. The magnet is positioned so the area where it loops over from the center to outside, where the field lines are roughly horizontal, is aligned with the bottom of the inner cylinder.
To create a spheromak, a small puff of gas is introduced to the area between the cylinders. A large electric charge supplied by a capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
bank is applied across the cylinders, ionizing the gas. Currents induced into the resulting plasma interact with the original magnetic field, generating a Lorentz force
Lorentz force
In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...
that pushes the plasma away from the inner cylinder, down into the empty area below. After a short period the plasma stabilizes into a spheromak.
Other common devices include open-ended or conical theta-pinch, where they were first researched in depth, and modern machines that generate them magnetically in a steady state.
Since the spheromak's magnetic confinement is self-generated, no external magnet coils are required. However, the spheromak does experience the "tilting perturbation" that allows it to rotate within the confinement area. This can be addressed with external magnets, but it is generally solved by wrapping the confinement area in a conductor, typically copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
. When the edge of the spheromak torus approaches the concudtive surface, a current is induced into it that, through Lens law, reacts to push the spheromak back into the center of the chamber.
It is also possible to get the same effect with a single conductor running down the center of the chamber, through the "hole" in the center of the spheromak. As this conductor's currents are self-generated, it adds little complexity to the design. However, stability can be further improved by running an external current in the central conductor. As the current scales up it approaches the conditions of a traditional tokamak, but in a much smaller size and simpler form. This evolution led to considerable research on the spherical tokamak
Spherical tokamak
A spherical tokamak is a type of fusion power device based on the tokamak principle. It is notable for its very narrow profile, or "aspect ratio". A traditional tokamak has a toroidal confinement area that gives it an overall shape similar to a donut, complete with a large hole in the middle...
during the 1990s.
See also
- field-reversed configurationField-Reversed ConfigurationA 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....
, a similar concept - spherical tokamakSpherical tokamakA spherical tokamak is a type of fusion power device based on the tokamak principle. It is notable for its very narrow profile, or "aspect ratio". A traditional tokamak has a toroidal confinement area that gives it an overall shape similar to a donut, complete with a large hole in the middle...
, essentially a spheromak formed around a central conductor/magnet
External links
- Spheromak activity at Caltech
- The Swarthmore Spheromak Experiment and its FAQ
- About the SSPXSustained Spheromak Physics ExperimentThe Sustained Spheromak Physics Experiment is a program at Lawrence Livermore National Laboratory in the United States to investigate spheromak plasma....
at Lawrence Livermore National LaboratoryLawrence Livermore National LaboratoryThe Lawrence Livermore National Laboratory , just outside Livermore, California, is a Federally Funded Research and Development Center founded by the University of California in 1952...