Day 1 of 5: Plasma Crash Course
I
have grown a great appreciation for air conditioning. The heat wave
has not held back and my Princeton dorm has no AC. It's no wonder
that Princeton offers no summer courses. But after my first day at
the PPPL, I can already tell this experience will be worth it. Our
first day of intensive plasma physics lectures has begun: O, how one
forgets how hot it is outside when one is trying to understand plasma
dispersion and turbulence...
My favorite quote from today's lectures came from the famous Werner Heisenberg, ?When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first.?
For those who are interested, I am going summarize (very briefly) my notes from today's lectures. This will reinforce the material for me as well as list some high points of plasma and fusion science for those who wish to know more about the subject.
Introduction to Magnetic Fusion ? Stewart Zweben, PPPL
Zweben's talk was basically split up into three parts: ?The Dream?, ?The Reality?, and ?The Future?. The Dream is the logic and optimistic outcomes of fusion reaction. You put Deuterium, a naturally occurring isotope of Hydrogen, and Tridium, a radioactive isotope of Hydrogen produced in the reactor from a Lithium ?blanket?, nuclei together by making them collide at energies as high as 20 keV (about 200 million degrees C) and you get 17.6 million eV out. Zweben stated, ?Deuterium in 1 gallon of water can produce the energy of 300 gallons of gasoline, if burned in a fusion D-T reactor.? Plasma tends to lose energy rapidly and cools down, but if an ?ignition? stage is reached, the energy in the plasma will be self-sustained. Ignition is possible, and we have observed it in our Sun and in the H-bomb. The Sun has confined plasma energy over a long time with gravity squeezing its mass tightly at the core. The H-bomb releases its energy all at once, an occurrence no one wishes to observe. Theoretically we can confine the plasma long enough for save ignition in the lab. Plasma ions and electrons helically revolve around magnetic field lines, and scientists have been able to design devices that bend the fields in such a way to keep plasma in a controlled space. Some popular designs are the Tokamak and the Stellarator. If we can confine the plasma long enough for ignition, then we can use the net energy flux of the reactor to heat fluid, exchange that energy to a turbine and generate electricity. In short, this is the most advanced plan ever proposed to boil water.
The Reality is that, ?... fusion is facing many serious scientific and engineering problems, and it is not yet clear that we can make a reactor.? The problems arise from the lack of ability to hold the plasma in long enough for ignition at the proper densities and temperatures required. Plasma transport is extremely difficult to understand due to turbulence. Pressure limits, confinement, maintaining steady-state plasma, and plasma-wall interactions are all problems facing a practical reactor.
The Future holds new inovations in plasma science with ITER and other Tokamak designs, better Stellarator designs, and a world wide effort to master magnetic fusion. Computational sciences are hopeful in finding optimum designs without costly experiments. Technological innovations like in superconducting technologies improve experiments. And we also hope for what Zweben calls ?physics surprises?.
Magnetohydrodynamics (MHD) ? Ben Chandran, University of New Hampshire
Magnetohydrodynamics or MHD takes a fluid modeling approach to understanding plasma. Chandran derived the single fluid equations for MHD and made the assumption of Quasineutrality in the plasma. After seeing how involved this ?simple? approach was, I as well as all of the other interns were surprised at how much Chandran could get into a one hour lecture. Quasineutrality is the assumption that the ion and electron densities are approximately the same and so the velocities are approximately the same. What's interesting is that the velocity is a function of both space and time in a fluid. This more complex definition of velocity makes sense if you have ever seen water go down a drain and notice water closer to the drain moves faster. Also, the pressure force in the fluid is simply proportional to the gradient of the pressure. If you have ever gone so deep under water that your ears have ?popped?, then you have a first hand experience with this pressure gradient.
Using these special terms of acceleration (from velocity) and pressure combined with the Lorentz force, Chandran showed a relation of plasma current to a magnetic pressure force and a magnetic tension force. The tension force has to do the resistance to pulling the field lines (much like pulling a rubber band). This equation is used to describe the momentum. A magnetic induction equation was derived using Ohm's law with the magnetic term added in.
The Frozen-in Law was discussed and is basically a statement that the plasma ?fluid? that is connected by two intersecting flux surfaces remain attached to a field line. So if you have two planes, both of which have magnetic fields pointing in the same direction, the plasma moves with the field lines, but at the line of the two planes' intersections, the plasma attaches to that field line. In fact, the plasma can change that field line due to turbulence making the field stretched and tangled. These changing field lines create low frequency Alfven waves that propagate transversely away from the plasma.
Single Particle Motion ? Bill Dorland, University of Maryland
In Dorland's talk, he derived the motion of ions/electrons in a plasma with uniform fields. The helical motion of an ion around a magnetic field (with no E field) can be simply found by setting the Lorentz force equal to the acceleration times mass. The perpendicular velocity divided by the cyclotron frequency is defined to be the Larmor (gyro-) radius. When an electric field is introduced, we changed our frames of reference to get a velocity at which we cannot ?see? an electric field. As it turns out, the solutions are similar, but there is now a new term in the velocity that has nothing to with mass, time, or any properties of the plasma: only the E and B fields. This term is called the ExB drift. And from this drift term we found what is called the drift velocity. These drifts result in plasma escaping magnetic field lines and hitting walls in plasma confinement chambers. This problem is hopefully solved in stellarator confinement, which is a twisted magnetic field as opposed to the circular fields in a tokamak. Stellarators hope to average out forces that try to let ions out of parallel and perpendicular confinement.
Turbulence and Transport ? Nikolai Gorelenkov, PPPL
We first reviewed some basics on random walks and mean free path theory to get a basic idea of gas transport principles. Diffusion is a problem in plasmas because, like gasses, they want to gain as much entropy as possible. For fusion, we want ions to collide, so diffusion is naturally the enemy. Parallel diffusion (along B field lines) is small due to the confining nature of the field. So perpendicular diffusion is of interest because magnetic field strength is responsible for how much the plasma is allowed to diffuse. But with a stronger field, Coulomb interactions increase turbulence. Eddies in these turbulent flows create changing diffusive gyro radii much like random walks. Gorelenkov showed some linear estimates to the diffusion rate equations and discussed some hopes of computational, theoretical models to help solve the behavior of turbulent flow, especially its internal structures.
Posted at 08:23PM Jun 09, 2008 by jlbarton in General | Comments[0]