Copasetic Flow

After working through the spherical solenoid models yesterday, I did a few more models on plain-old solenoids to see how well we could do by just extending the length of the solenoid.  Given that your Dewar is about five feet tall and our sample is at most six inches in diameter, we have plenty of room to wrap a solenoid that is several times longer than the sample.  The graphs below show the percent variance between the maximum field at the center of the solenoid and the field at the edge of the spherical lead sample for the direction parallel to the solenoid, (second picture), and the direction perpendicular to the solenoid, (third picture). So, for the amount of effort required, the solenoids look like the easiest thing to construct with better results than the spherical coil.  The downside is that the 4 X long solenoid will require more superconducting wire and more liquid helium to fill the Dewar, both of which are sort of pricey.

Working on modelling the magnetic field that will be used to quench a 4 inch lead superconducting sphere in the h-ray experiment.  The first trial was just to place the superconductor in a surrounding solenoid electromagnet.  The correct magnitude of field can be obtained that way, but the uniformity isn't great.  Adding more layers of windings increases the field strength but doesn't help with the uniformity.  Each level of coils basically linearly increases the field strength.  The percent change in field with length along the solenoid, (shown on the x axis below), stays pretty much the same though.  The graphs shown are for one, two, and three layers of coils. While looking around for a coil design that would give a more uniform field I came across a patent[1] that described a spherically wound electromagnet and promised a uniform field within the sphere.  I tried modified the model to handle a spherically wound coil and got the results along t...

When working on our latest research project which involved solving relativistic mechanics problems, we were surprised to find out that we'd been scooped on our relativistic rocket problem example by seven year.  It was very cool, though, to find out that not only was the article that scooped us excellent, but that the author was in fact astronaut physicist Ulrich Walter! You can read more about him at Wikipedia: http://en.wikipedia.org/wiki/Ulrich_Walter and on his university web page: http://web.lrt.mw.tum.de/index.php?id=119 His relativistic rocket article is behind a paywall, but if you're at a university library, the link is http://www.sciencedirect.com/science/article/pii/S0094576506001433 References 1. Walter U. (2006). Relativistic rocket and space flight, Acta Astronautica, 59 (6) 453-461. DOI: 10.1016/j.actaastro.2006.03.007

This is what Elaine and I have been working on in our spare time the last several months. Basically we demonstrated that solutions to non-relativistic mechanics problems could be transformed to their special relativistic counterparts using hyperbolic trig. We also found a much simpler way of deriving how electrons move around atoms ala the Thomas precession when taking special relativity into account. Then we got to make a pretty picture of it all!

Just a note about vacuum radiation and similarities Casimir When we solve for Casimir energy, we first quantize a field in free space and ask what frequency modes it can support.  The answer is all of them because free space is isotropic and homogeneous.  We then put in boundaries, either conducting or dielectric, and then as what frequency modes the space between the boundaries can support.  The answer will in general be different because the boundaries change what frequency modes can be supported.  For example, with parallel conductors, only the modes that can fit multiple half-wavelengths perfectly between the conductors will be supported. Fulling-Unruh Radiation It's wasn't immediately apparent to me, but Fulling-Unruh-Hawking radiation is a very similar process.  The first step is identical: solve for the available frequency modes in free space.  The second step is to solve for the modes in a new space-time coordinate system.  A Bogoli...

I'm back in the lab this week working on some numerical models for the solenoid to be used in the H-Ray experiment.  In looking for analytic solutions for the z and rho components of a magnetic field due to a coil, I came across a very interesting reference in an article by Bergeman, Erez, and Metcalf[1].  Take a look If you're one of the many who after poring over Jackson, thought "This can't be right", in this one case, you were right.  The proper expressions according to Bergeman et al. are Hyperbolic Bessels Solving for quantized fields, one is often led to Bessel eigenfunctions in cylindrical coordinates.  Based on some of my recent work, I was left with the feeling that relativistic quantizations of the field in a uniformly accelerated space might give the result in terms of hyperbolic Bessel functions.  Sure enough, the Macdonald function solution that Dr. Fulling[2] finds in his paper "Nonuniqueness of Canonical Field Quantization in Ri...