Caylin Mendelowitz and Brian Carlson

Fusion

The idea of fusion was first considered when scientists realized the amount of energy released from the combination of light nuclei. Fission, the separation of heavy nuclei, also releases a lot of energy but it is highly unstable and radioactive. If confinement of a fusion reaction could be achieved, it would be a relatively harmless way of producing commercial energy. It would provide almost limitless energy. Deuterium is readily available in seawater and could sustain fusion power for millions of years. It is estimated that fossil fuel reserves will only sustain the energy needs of our society for another 50 to 100 years. More conservative estimates say that the production will start to severely decrease by the 2010 (Campbell, pg. 79). Given these estimates and the increasing energy needs of our society, a new alternative is needed. Fusion offers an alternative.

Reactions Involved

The energy released in a fusion reaction is due to the mass defect that occurs when two light particles are combined to form a heavier atom. It turns out that the individual masses of the particles before they combine is greater than the mass of the nucleus after the reaction. During the fusion process the mass difference is converted into energy, in accordance with E= mc². This is the mass defect. It turns out that this defect is higher, and thus more energy can be produced, with lower atomic number (Z) elements. Since there is no mass defect with hydrogen, we look to isotopes of hydrogen (Hagler, pg.4).

To get nuclei to fuse they have to overcome the Coulomb repulsion. Because of their like charges the protons will repel each other with a force=k(Z₁q₁Z₂q₂/r²), where k is the Coulomb constant, Z is the atomic number, q is charge, and r is the separation between nuclei. From this we can see that it is easier to overcome the Coulomb repulsion with smaller Z elements. This is another reason that smaller Z elements are preferred.

There are many fusion reactions that have been considered for fusion power. One reaction that has been used in recent fusion experiments has been the deuterium and tritium (D-T) reaction. This reaction produces a helium atom, a neutron, and a mass difference, which corresponds to an energy release of 17.6 MeV (see reactions below).

The most common fuel in fusion experiments is 2 atoms of deuterium (D-D), which fuses in several steps (see reactions above).

The D-T reaction occurs at a lower temperature, about 100 million K, and has a breakeven temperature of 4 keV which is lower than the breakeven temperature for D-D is 40 keV (breakeven is when the energy input is equal to the energy output). D-T fusion can be achieved with weaker magnetic fields than D-D and has a shorter confinement time for fusion than D-D (Fowler, pg. 8). For this reason it is easier to achieve fusion with D-T, making it the better choice given the current confinement and heating technology.

However, there are some advantages to the D-D reaction. Deuterium is extremely easy and relatively inexpensive to obtain. A single atom of deuterium is found in seawater for every 6500 of regular hydrogen. Tritium on the other hand must be manufactured from lithium and is more expensive to produce. It is radioactive with a half-life of 12.4 years. The D-T reaction gives off a neutron which, having no charge, escapes the magnetic confinement and is absorbed by the walls of the reactor. This turns the metals in the wall into radioactive isotopes that need to be periodically replaced. (Fowler, pg. 6-10).

The D-D and D-T reactions are referred to as primary reactions. After the primary reaction another reaction takes place called the secondary reaction. In future reactors, a blanket of lithium surrounds the plasma. As neutrons escape they will enter this layer and be absorbed in the secondary reaction. Natural lithium is made up of 7.5% ⁶Li and 92.5% ⁷Li and thus two different tritium producing reactions occur (see reactions below)(Stacey, pg.1).

Which reaction occurs depends on the speed of the neutron. Slower moving neutrons would react as in the first equation and faster neutrons as in the second. Once fusion is underway, this reaction acts as the tritium production mechanism.

Confinement

Containing a plasma that is hundreds of millions degrees Kelvin is difficult task to achieve. As the plasma is heated it tends to expand. We can not contain the plasma with material walls because no material can withstand temperatures above 3500 K (Hagler, pg.7). But more importantly than our scientists being scorched and becoming radioactive, is the fact that when the plasma touches the walls of the reactor it would cool down by losing energy to impurities. The two main designs that are being pursued to overcome this are inertial confinement and magnetic confinement.

Inertial Confinement

One of the first mechanisms used to try to confine the fusion reaction was inertial confinement. The basis of inertial confinement is to somehow apply intense uniform pressure on all sides of a D-T fuel pellet. This causes the pellet to implode in on itself, reach temperatures of 100 million K, and begin fusion. This technique was first used in designing the hydrogen bomb. In the hydrogen bomb the mechanism used to implode the fuel pellet was a well-calculated fission reaction. The fission reaction had to implode the fuel pellet with perfect symmetry. For a controlled reaction, researchers use different trigger mechanisms such as lasers or ions. The problem with inertial confinement is that it keeps the pellet together only if the distribution of the laser light is extremely uniform. This makes inertial confinement hard to do on a large scale. For example, in the National Ignition Facility (NIF) inertial confinement experiment at the Lawrence Livermore National Laboratories 192 lasers will be used to attempt to make this design work. Although inertial confinement has begun to show some promise in the race for fusion energy, the primary candidate, and the one in which this paper will be concerned with is magnetic confinement (Duderstadt, pg. 3-5).

Magnetic Confinement

One of the proposed designs for confining the plasma was a magnetic field configuration. Charged particles experience a force from the magnetic fields as seen in the Lorentz force equation: F=qv x B in the absence of an electric field (qE=0). From this equation and the right hand rule for particles in a magnetic field we see that the particles are confined to helical paths along the field lines (Halliday, pg. 738-40). Different charges are going to spin in different directions. Electrons will move in a counterclockwise path, ions in a clockwise path (see diagrams).

The radius of this helical path around the field line is inversely proportional to the strength of the field. The stronger the field the smaller the radius. This radius is called the Larmor radius (see derivation) (Chen, pg. 20-21). Notice that the radius of the helical path is also proportional to the mass. Since the mass of a proton is larger than that of an electron, protons will spin in larger circles than electrons.
 

Magnetic Mirrors

Although the particles are confined  along the magnetic field lines, they are not confined at the ends. So, another configuration is used to confine them in this way. By making the magnetic fields stronger at the ends of the cylinder, a field gradient is created (see diagram).

This is called a min-B configuration. The magnetic field is created by loops of current around a solenoid. These loops induce a magnetic field through the hole in the cylinder. The tighter the coils are wrapped, the stronger the magnetic field. By wrapping the coils tighter at the ends a stronger field is induced, thus creating our magnetic bottle (Glasstone, pg. 61-62). The stronger magnetic field produces a decelerating force on the particle along the field line. This causes the particle to fall back into the region of weaker magnetic field, and hence trapping it in this region. But the particle doesn’t just reverse its direction along the field line it’s on. Instead, a force from the magnetic field in the vertical direction gives it a kick up (or down) a field line, so that the particle ends up travelling in the cylinder in a closed loop path. The problem with this model for confining the plasma is that eventually, through collisions, all the particles will gain enough energy to escape from the confinement. So, to eliminate this problem of particle loss a design with no ends is created. (Hagler, pg. 71-74).

Toroidal Configuration

To eliminate the problem of escaping particles, researchers decided to use a donut shape reactor. The magnetic field is created in the same way, by wrapping wires around the donut. Since the coils are more closely spaced on the inside of the donut than the outside, there will be a stronger magnetic field on the inside than on the outside (see diagram below).

As we have seen the radius of the helical path decreases as the magnetic field increases. The magnetic field gradient in the torus will cause the particle to orbit with a larger radius on the weaker side and a smaller radius on the stronger side (see diagram below).

This causes the particles to drift up the field lines if they are electrons and down if they are ions. This is called grad B drift (Chen, pg. 26-28). When the particles separate they create an electric field in the direction of the ion motion. The force from the electric field in combination with the magnetic field causes them to drift into areas of weaker magnetic field. This is called E x B drift (Chen, pg. 23). To eliminate E x B drift we need a new design.

Correcting E x B Drift

E x B drift is caused by the electric fields. So we need to suppress the electric fields. By twisting the magnetic fields, we create a net cancellation of the electric field. This produces what is known as a sheared field. To produce a sheared field we create two different magnetic fields. In addition to the toroidal magnetic field, which runs through the torus, a poloidal magnetic field arises from a current through the plasma is established. The production of this current will be explained later. (Stacey, pg. 4-7)

This creates new microinstabilities. The shearing of the magnetic field lines keeps the particles from drifting, but at same time creates little magnetic mirrors within the torus. Normal collisions can cause the particles to jump field lines, but only as far as 2 times their Larmor radius allows. Collisions within these mini magnetic mirrors are more of a problem because now the particles can jump the width of the mirror. This allows the particles to escape the magnetic confinement faster, since their jumps are bigger. (Chen, pg. 193-194)

Methods of heating the plasma

Along with creating the poloidal magnetic field, the toroidal current also goes to heating the plasma. This ohmic heating only serves to heat the plasma part of the way to the temperature needed for fusion. Resistance in the plasma occurs from collisions between electrons and electrons and ions. The probability of such collisions occurring decreases with increasing electron velocity. So, the resistance of a plasma will decrease with increasing temperature. Therefore, other methods must be utilized to further heat the plasma. (Stacey, pg. 69-70)

Injecting a neutral beam of deuterium particles can also go to heating the plasma. In this process a neutral beam of high energy D (it has to be neutral to penetrate the field lines) is directed at the plasma. (Stacey, pg. 70-74)

Another method of heating is through radio frequency bombardment. The radio waves are sent into the plasma with a frequency that will resonate with the frequency of the radiation produced from the cyclotron motion of the ions. (JET, http://www.jet.uk/fusion4.html)

Yet another method of heating is called Lower Hybrid Current Drive (LHCD), which refers to particular waves excited in the plasma. In this situation, microwaves are sent into the plasma, accelerating the electrons to generate a current. (JET, http://www.jet.uk/fusion4.html)

When enough helium is produced from the fusion reactions to sustain the proper temperature of the plasma, the reaction is considered to be self-sustaining. At this point the reaction is considered ignited. (JET, http://www.jet.uk/fusion4.html)

Main reasons for energy loss in the system

When conditions for confining individual particles are applied to confining plasma, many difficulties arise. Two of the primary complications in confining plasma are collisions between particles and plasma instabilities

A confined plasma tends to spread out and escape its magnetic confinement. This is called diffusion. Instabilities provide a way for the plasma to "punch holes" in the magnetic confinement and escape. Instabilities can be classified into two groups: magnetohydrodynamic (MHD)/macroinstabilities or microinstabilities.

Magnetohydrodynamic instabilities cause ions and electrons to move together like a fluid. This results in gross motion of the plasma that can cause the plasma to bump into the walls of the chamber. When the plasma interacts with the walls it can be cooled down, or become contaminated with impurities from the wall. Creating a magnetic field with a minimum at some point and increasing in every direction, the min-B configuration, can eliminate these instabilities, although the toroidal configuration does not because of the nonuniform magnetic field. (Hagler, pg. 14)

Another problem that arises when confining plasma, are the energy losses due to radiation. When charged particles are accelerated they give off radiation. The particles can be accelerated in two ways, each resulting in a different kind of radiation. Particle repulsion/attraction causes acceleration. The radiation produced from this motion is called Bremsstrahlung (Brems=braking, strahlung=decelerating) radiation. (Glasstone, pg. 26)

When the particles move in helical paths around the field lines this also gives off radiation called synchrotron radiation. Since the magnitude of acceleration is a=F/m and F=q(E+vxB), m is much smaller and v is much larger for an electron than for an ion. Thus the electrons are accelerated much more and are therefore the dominant source of radiation.

Bremsstrahlung radiation from electrons is in the form of x-rays. Since the plasma doesn’t absorb this wavelength of radiation, it will often have to be collected somehow. Radiation from synchrotron radiation comes in the form of infrared and microwaves. Since the plasma will absorb this wavelength of radiation, the primary energy losses due to radiation will be in the form of bremsstrahlung. (Glasstone, pg. 37-38)

Correcting Macroinstabilities

Since the toroidal configuration has more advantages it is preferred over the min-B configuration (magnetic mirrors). This means that since the MHD and diamagnetic properties of the plasma cause it to drift towards areas of weaker magnetic field, the plasma is now going to drift to the outer edge of the torus and eventually escape confinement. To counterbalance this drift motion another magnetic field is created. A vertical magnetic field through the cross-section of the donut is produced by a series of toroidal current loops around the outside of the donut. This magnetic field, in conjunction with the toroidal current, creates a force pushing inward from the outside of the donut. This force is shown in the right-hand-rule and the Lorentz force equation: F= qv x B. These toroidal currents on the outside of the donut also go to indirectly creating the internal toroidal current. A varying current is set up in the middle of the torus. This current sets up a magnetic field through the donut hole, which induces the internal toroidal current. (Hagler, pg. 59)

D-T Reactor

The neutrons

When deuterium and tritium fuse, the energy produced is in the form of high-energy (14 MeV) neutrons (see reaction section). In order to get usable energy out of the system the kinetic energy of the neutrons has to be converted into electrical energy. This is achieved by first converting their kinetic energy into heat. The neutrons are also used in the production of tritium (Hagler pg. 31-32). These reactions are called secondary reactions and were discussed in the reaction section. (Glasstone, pg. 42-43)

Removal of fusion products

The waste products, such as Helium, produced in the fusion reaction need to be removed because they increase bremsstrahlung radiation. This can be accomplished using a magnetic field arrangement called a divertor. The divertor is designed to scrape off the outside layer of the plasma and guide it, using magnetic fields, out of the reaction. Then it is reused as fuel. (Glasstone, pg. 310-311)

Tokamaks

The design for the reactor must have features that accommodate all of these considerations. The most critical property of the reactor is the composition of the wall surrounding the plasma. It needs to be relatively transparent to the neutrons so they can filter through to the lithium layer and be used to produce energy and create tritium. It also must be able to withstand exposure to the bremsstrahlung, synchrotron, and gamma ray radiation. Outside the first wall is a layer for neutron absorption, tritium production and heat transfer. There are also features to protect the superconducting magnets from gamma ray and neutron radiation. Extreme care must be made to keep the heat of the plasma insulated and not affect the cool temperature of the magnetic coils. Since there is such an extreme temperature difference between the plasma and the magnets, each layer of the torus is thermally insulated. (Hagler, pg. 36)

Future

Fusion researchers have made some excellent progress over the last 45 years of research, but there is still no guarantee of commercial fusion anytime in the near future. Lack of funding is slowing down the building of new experiments that may offer new insights on overcoming the current problems in the tokamak design and learning more about the confinement of plasma.

However, researchers remain optimistic. The importance of fusion energy is once again starting to be recognized by government agencies and researchers are coming up with less expensive experiments that will help the field progress. At a recent fusion meeting in Madison, WI researchers optimistically discussed an alternative approach which would involve many smaller experiments. Many less expensive experiments, whose goal would be a further exploration of the physics involved with a burning plasma, would be built instead of the proposed 10 billion ITER project.

Many researchers feel that fusion will be commercially viable by the middle of the next century. With fossil fuels running out and the energy needs of our society increasing, it is imperative that new clean energy sources are found. Fusion offers that potential.

Books