A plasma is a state of matter, like a liquid or a gas. A plasma is like a gas in that the atoms are not constrained to a constant volume by chemical bonds. However, in a plasma the atoms are also ionized, meaning that the electrons have enough energy to escape their nuclei. Plasmas are extremely common in space, but can also be found on earth. Lightning is the ionization of air between a charged cloud and ground. In SSX, we ionize hydrogen using a high voltage and current to create a plasma of protons and electrons.
Plasmas are a type of fluid, and fluids display complicated turbulence. Physicists have a good understanding of the rules by which one or two individual fluid particles interact. However, when huge numbers of particles come together, we cannot predict what will happen even with the best mathematical models. Just as moving air can form interesting structures like tornadoes or the jet stream, plasmas can also form unusual structures which cannot be predicted by solving equations. Plasmas are even more complicated than "neutral" fluids like air, since they are good conductors of electricity. Electric and magnetic fields can affect the motion of particles in a plasma, and this motion in turn affects the electric and magnetic fields. In addition, the electrons and nuclei can be thought of as two separate fluids. Thus, the dynamics of plasmas are difficult to predict and understand without actually looking at an experimental system.
At SSX, we are looking at the interesting plasma structures that appear in a particular geometry of particles and fields: reconnection between spheromaks. This arrangement is an important one to investigate, because it is a scaled-down version of structures that appear in space. For example, coronal loops on the surface of the sun are much like SSX plasmas. We may be able to answer questions about the sun from here on earth. Also, basic research about plasmas will contribute to the development of fusion power, an environmentally friendly source of energy.
A spheromak is a toroidal ring of plasma in equilibrium according
to basic MHD equations of motion; it is a good source of stable magnetofluid
for reconnection experiments. The plasma contains helical currents and
magnetic fields that are continuous around the toroid. The figure below
shows the magnetic fields decomposed into the poloidal and toroidal components.
The toroidal field runs the long way around the toroid and the poloidal
field runs the short way around the ring. Although they are not drawn in
this figure, the current that generates these fields is also helical.
The magnetic fields confine the plasma according to the frozen-in flux
constraint, but if there were nothing to contain the magnetic field, the
spheromak would expand infinitely just as a puff of gas in a vacuum does.
SSX uses a copper cylinder `flux conserver' to contain the magnetic fields.
As the field encounters the copper wall, image currents flow in the copper
according to Faraday's law and prevent the magnetic field from passing
through the wall.
Magnetic reconnection in magnetofluids is the process by which
lines of magnetic force break and rejoin in a lower energy state. The excess
energy appears as kinetic energy of the plasma at the point of reconnection.
This figure is a schematic of magnetic reconnection. Single line arrows
are magnetic field and double line arrows indicate magnetofluid flow velocity.
The merging of two magnetofluids with oppositely oriented magnetic fields
causes the fields to annihilate. The excess energy accelerates the plasma
out of the reconnection region in the direction of the long double line
arrows. Note the characteristic X-point where the topology changes for
two field lines.
The reconnecting field lines form an X-point at the center where the topology changes from being connected horizontally to being connected vertically. The double arrows show flow velocity, indicating that parcels of plasma with oppositely oriented magnetic fields are merged together. The oppositely oriented magnetic field vectors annihilate each other. By conservation of energy, the plasma where the field was annihilated is accelerated outwards to a characteristic speed, called the Alfvén speed. Conservation of energy does not, however, specify the detailed structure of the magnetic field in the reconnection region or provide a physical mechanism for the breaking of field lines. Many theories have been proposed to answer these questions.
There is growing evidence that reconnection processes control the release of energy into the solar corona. Coronal loops have strong currents flowing through them and are confined by their own magnetic fields. Recent satellite observatories such as Yohkoh and SOHO have produced dramatic images of coronal loops in hard and soft x-ray as well as visible light. Using these instruments, Masuda et al. (1994) identified the spectral signature of particle acceleration due to magnetic reconnection at the top of the coronal loops. According to his theory, the coronal loop is distended by buoyancy. A magnetic structure is buoyant because it exchanges lower particle density for a larger magnetic energy density (which doesn't weigh anything). The external (surface or coronal) pressure is therefore balanced by a lower gas pressure in conjunction with a magnetic pressure. Since it has lower density, it is buoyant.}, which causes the top of the loop to distend and reconnect as shown in the figure above. Particles in the reconnection region accelerate towards the surface of the sun and out away from the sun. Those particles that are accelerated back towards the sun are confined within the loop's magnetic field and follow the field lines down to the footpoints of the loop where the accelerated particles collide with other particles and lose their energy through x-ray emissions.
The emission of energetic particles at the top of the loop may help explain why the corona (upper atmosphere) of the sun is three orders of magnitude hotter than the surface of the sun. Measurements of emission spectra show that the surface of the sun is about 5400~K while the corona is more than 10^6 K. It is not possible to explain this temperature difference by thermodynamics alone. Magnetic reconnection provides a mechanism for energy to be transported into the solar corona in the form of magnetic energy and then converted into kinetic energy. A coronal loop such as the one in the above figure is the most visible manifestations of this energy transport mechanism.
Magnetic reconnection is also important in the physics of the earth's magnetotail. The solar wind distends the earth's dipole magnetic field so that the field extends behind the earth for many earth diameters. The picture is the same as that shown for the coronal loop in the figure above with the surface of the sun replaced by the earth's dipole magnetic field. Earthward flowing plasma streams with flow velocities up to 1000 km/s (close to the local Alfvén speed) have been observed after reconnection events in the earth's magnetotail (Birn et al. 1981).
A Magnetofluid is an electrically conducting fluid or dense plasma. Magnetic fields due to currents flowing in these conducting fluids modify the flow of the fluid itself according to the Lorentz force. The resulting dynamics are called magnetohydrodynamics (MHD). One important feature of MHD plasmas that are highly conductive is that any magnetic field that is imbedded in a parcel of magnetofluid must remain attached to that parcel no matter how convoluted the field topology may get. If the field were to attempt to move with respect to the fluid, Faraday's law states that currents will flow in the fluid to maintain the original magnetic field. Solar flares, the solar wind, the earth's magnetosphere, liquid metals and high density laboratory plasmas are examples of magnetofluids.
The figure below shows a visible light picture of a coronal loop emanating from the surface of the sun. Coronal loops have strong currents flowing through them and are confined by their own magnetic fields. The sun and many planets have liquid cores that are filled with conducting fluid. The spin of the planets generates the planetary or solar magnetic field through a mechanism called the magnetic dynamo effect. The magnetic dynamo depends on a complex current and fluid flow structure inside the sun or planet. Coronal loops may be the visible evidence of such current structures. There is growing evidence that reconnection processes control the release of energy into the solar corona. The strong magnetic field energy carried in the coronal loops is dissipated in the corona by magnetic reconnection.
SSX uses magnetized coaxial plasma guns to create spheromaks.
The schematic above shows how the formation process works. A puff of gas
via the Kornack valuve is introduced into the annular gap between the inner
and outer coaxial cylindrical electrodes (a). High voltage capacitors charged
to 5-10 kV are connected to the electrodes and cause the gas to ionize
and become a toroid of plasma. Current flowing in the gun and through the
plasma interacts with its own magnetic field to produce a J x B
force which accelerates the plasma towards the open end of the gun (b).
The same acceleration mechanism is found in a typical rail gun. A strong
magnetic field, called the 'stuffing field', is produced by an external
magnetic coil and is concentrated in the center electrode with a slug of
high permittivity metal. The plasma encounters this magnetic field at the
opening of the gun and resists the change in field according to Faraday's
law. Because plasma is an excellent conductor, currents flow in the toroid
of plasma as the it distends the stuffing field (c). If the magnetic pressure
from the gun exceeds the magnetic tension of the stuffing field, the toroid
breaks away to form a spheromak. The field lines distend and then reconnect
in back as the spheromak forms. The Spheromak inherits toroidal field from
the gun field and poloidal field from the stuffing field (d).
The process is analogous to blowing a soap bubble. The soap film tension
represents the stuffing field strength and the pressure of one's breath
represents the magnetic pressure of the gun current. A soap bubble is formed
when the breath's pressure overcomes the surface tension of the soap. The
amount of gun current (breath) required to overcome the stuffing field
(soap film) is called the formation threshold. An appendix in the Magnetic
Reconnection Studies on SSX is devoted to the detailed study of the
formation threshold for coaxial plasma guns.
After formation, the spheromak is not in equilibrium with the field, pressure and current profiles imposed by the coaxial plasma gun. Reconnection allows the fields to rearrange themselves towards a minimum energy state. The equilibrium of a spheromak is essentially the lowest energy configuration of the magnetic fields with pressure forces on the plasma.
Spheromaks more convenient to create and use as sources of magnetofluid and because they are somewhat collisionless, the magnetic reconnection will show interesting details. Magnetic reconnection is generated by merging two spheromaks, which are unlinked toroidal configurations of magnetofluids. Spheromaks have large magnetic fields and low pressure effects, making them a good candidate for magnetic reconnection studies because the reconnection must occur in a plasma that is essentially collisionless. Whereas resistive collisions are believed to be the mechanism for reconnection in collisional plasmas, scientists do not know the mechanism for reconnection in collisionless plasmas. The low-density, collisionless nature of spheromaks make them a good source of plasma for the study of the unknown mechanism of collisionless reconnection. Because the spheromak is unlinked, the spheromaks can be created at the ends of the vacuum chamber and then translated to the region in the center where the experiment takes place. This freedom allows the sources of electromagnetic noise in the spheromak formation regions to be removed from the experiment. Tokamaks, stellerators, and many other plasma confinement schemes are linked by the device and cannot be moved so easily.
