# Ambit Magnets

The Merriam-Webster Dictionary gives the first meaning for ambit as "CIRCUIT, COMPASS." The other meanings are "the bounds of limits of a place or district" and "a sphere of action, expression or influence."

## Why a Continuous Rotor

JKM: The key thing is the rotor's use as a heat sink. It therefore has to be simple and can't carry the smarts I wanted it to. I applied many of these arguments in reverse, seeing the need for a continuous line of permanent magnets in the tubes. Either the fixed part or the moving part has to be continuous. I do not seem to be able to find another solution to the problem of heat, and I can't find my earlier notes, which is where I thought I had solved it. Everything else you say follows.

KHL: Ultimately, all heat dissipates through the tube/track, as non-contact thermal radiation. The rotor radiates to the track. Your writing got me thinking about the VelocityTransformer , and my unverified hunch is that stationary coils on the track can be used to couple energy more efficiently to the vehicle - less heat to get rid of. If the stationary coils can be made to heat instead of the rotor, they can connect to far more radiant surface.

I thought more about why I chose a continuous rotor 30 years ago (memory lane has some gaping potholes in it!). The problem is that the energy field ( B^2 / 2 \mu ) is much smaller when space is occupied by a ferromagnet than when it is empty. This energy change must flow as power into and out of the coils making the D magnets for the ambit. If 5 cm bolts moving at 10km/s have a "nose cone" only 10 centimeters long, and the ambit magnet field is 1 Tesla, then a volume of 200 cubic centimeters changes from an energy density of 400KJ/m3 to 0 in 10 microseconds, an average power level of 80J/1E-5s or 8 megawatts, taken from the coils in front and added back to coils in the back of the bolt.

It will be more complicated than that, as an open gap will have a high H field and a low B field, and the appearance of a bolt will cause both a negative dH/dt and a positive dB/dt, both of which will do wacky things to the voltage and current on the segment of the D magnet. The ferromagnetic bolt will carry field with it, and that will help with the dH/dt, but there will still be a large dB/dt on the magnet segment, which the controller must absorb.

If we clamp the controller voltage to zero, or use a closed-coil superconducting magnet, then the field will resist change. My intuition tells me that this will tend to demagnetize the front of the bolt, as well as force it away from the D magnet poles, putting quite a large repulsive yawing force on the bolt. Unfortunately, the tail end of the bolt will be subject to an attractive yawing force (sounds risque, doesn't it), so the overall effect will be to cause the bolt to yaw, lose coupling in the front, and smash into the magnet poles on the back.

Or perhaps my intuition is incorrect here. Still, I have labored to reduce the magnetic discontinuity on the sliding joints between rotor segments as much as possible because of this. Every peak watt I add to the controllers costs money I would rather save. Power electronics is not free.

## Superconductors

Superconductors seem magic to the general populace. I did my graduate work with superconducting Josephson Junctions at U.C. Berkeley, working under Ted Van Duzer. The annual IEEE prize for advances in superconductivity is named the "Van Duzer award". Although I cannot claim great expertise in 2011 superconductors (I graduated before the cuprate superconductors appeared), I did learn to respect their limits, as well as detect bad measurements masquerading as superconducting effects. TVD and I still meet every few years, and catch up with what is going on in the field.

The main thing to know is that a superconducting coil sustaining a high magnetic field is energetically metastable. If even a tiny bit of the material turns non-superconducting, either because of a local field concentration or a temperature fluctuation, it will be subject to ohmic heating and the temperature will increase. That can turn neighboring regions non-superconducting. The effect spreads rapidly, until the whole coil (still containing ragingly huge currents) is non-superconducting. The currents dissipate in ohmic heating, turning all the field energy into heat. If the energy is high and the heat sink is small, this will vaporize the liquid helium and create explosive pressure waves. This is called a magnet quench, and can rip a magnet and its containment to shreds.

Magnet quenches are minimized by not pushing the limits. The magnet material should be shunted with a lot of high purity, low resistance copper, which provides both heat sink and a path for currents diverted from fluctuations. High-TC superconducting materials have higher ohmic resistance in the normal state than lead and niobium and other metallic superconducting alloys, so the fluctuations are bigger. I don't know about their thermal conductivity, but if that is lower that also makes the fluctuations bigger. Lastly, High-TC superconductors are more like ceramics than metals; they are not ductile, very brittle, and have a different mechanical temperature expansion coefficient than metals (like the copper shunting material). All that means that real magnets can be made with high performance, but not nearly the performance that critical field measurements suggest to the naive.

In fact, the highest DC field magnets (around 15T) are still made with chilled copper coils, and the highest transient fields (around 100T) are made by crushing such coils with explosives. One reason for the cancellation of the U.S. Superconducting Supercollider in 1993 was their overly ambitious magnet design. The LHC uses a more conservative design, but a welding error in one of those magnets caused a quench, dozens of destroyed magnets, millions of dollars of destruction, and 6 months of downtime. The energy stored in the beam of the LHC is about that of a short high speed train - 360MJ. That is, the same energy as is stored in 120 centimeters of launch loop rotor ( 3kg/m, 14 km/s ).

The defining characteristic of any superconductor is the Meissner effect, their tendency to behave like perfect diamagnetic materials. The Type II superconductors are only approximately diamagnetic, some portion of the magnetic flux present when they are chilled to superconductivity gets trapped in the material - pinning. This is why a magnet will float on top of a superconducting surface, pinned in position and orientation. Rather spooky.

While a diminuation of resistance is characteristic of a bulk sample chilled below its superconducting temperature threshold, that is not defining. Most materials (metals and other) with large quantities of free electrons in the conduction band get less resistive with temperature, because thermal scattering reduces. Many materials undergo phase changes, shrinkage, and other effects. If a 4 point probe is measuring a cooling surface, the electrodes can skip across the surface as it shrinks or bends. Cracking can occur, or cracks can heal if the substrate shrinks more than the test material on its substrate. Noise in measurement equipment can add bumps and wiggles to resistance versus time logs. So even large changes in apparent resistivity are not sure proof of superconductivity. Without Meissner transitions, or persistent currents in rings of test material, it is difficult to tell what is going on.

The highest T_C superconductor is either Bi2Sr2Ca2Cu3O10 (BSCCO, or "Bisko") at 110K, or the recently announced HgBa2Ca2Cu3Ox at 133K. Any newly announced superconductor is treated with extreme skepticism by the condensed matter community - disproved claims are the norm, not the exception, in this field. The maximum currents and fields go down with temperature, so magnets using these materials are typically chilled to a fraction of T_C - 40K for Bisko, resulting in a current density of 5E5 A/cm2. Although the upper critical field is 200T, the "irreversibility field" is closer to 2T. YBa2Cu3O7 (YBCO) has a T_C of 90K, and an upper critical field (at 4K) of 250T, but again, the irreversibility field is much smaller, and the inability to make large single-crystal structures prevents their use in high current coils. These materials are useful to make sensing coils for superconducting quantum magnetic interference detectors - SQUIDs. But production superconducting magnets use older, more proven, and more stable materials in coddled environments.

Soon after the high T_C "gold rush" was underway, professor TVD participated in one the many superconducting startup companies. It folded, like almost all its competitors. There are still one or two around, still peddling magic to the credulous, usually failing to deliver.

Enter the charlatans and fools. There is one fellow, Joe Eck, who is continually announcing "record" high T_C materials. He does not demonstrate Meissner effect, he does not even prepare quality surfaces and do 4 point probe and microscopic crystalline evaluation. Instead, his samples appear to be prepared in a bench vise, and his "Kelvin probes" look like stacks of battery cables, with current passing through the inner contacts. His evidence of superconductivity is 0.4% jumps in "resistance" chart recordings, with the claim that the whole sample is not superconducting, but some crystals somewhere in it are. This is reminiscent of the old joke about the little boy cheerfully shoveling into a huge mountain of horse manure - "there's got to be a pony in there somewhere!". Eck might be a persecuted genius and the discoverer of room temperature superconductivity, but I would not bet on it.

So, pardon me if I am not overly excited about superconducting ambit D magnets. They seem like a quick path to failure.

## But Don't Higher Fields Lead to Smaller Ambits?

Yes, the 8.4 Tesla fields in the Niobium-Titanium magnets in the LHC are impressive. But we can't make a rotor or a bolt out of superconductors - there is no way to cool them. We are stuck with plain old ferromagnetic materials like steel. Steel has a saturation field of around 1.7T at room temperature. At higher temperatures, this diminishes, and goes to zero at the Curie temperature. At maximum launch loop rotor operating temperatures ( perhaps 500C ), 1T is a more reasonable saturation field. Steel will still appear approximately ferromagnetic far into saturation - it will still preferentially divert perhaps 2T of the field, compared to free space, but the magnetic deflection force of an 8 Tesla magnet will not be 64 times the deflection force of a 1 Tesla magnet. I don't have measurements (and it would be good to get them), but I suspect that the deflection force for an 8 tesla magnet is less than 4 times that of a 1 tesla magnet. At enormous expense and risk.

The hypothetical 4K magnets are millimeters away from an 800K rotor. The black body thermal flux across the gap is enormous, and the heat from a plasma sputtering cascade could create local hotspots that could easily trigger a quench. Every watt we pull out of the magnets and exhaust to a 300K ambient will require at least 75 watts of cooling at Carnot efficiency, more like 300W/W for realizable practical refrigerators. It will be very difficult to hot-swap and repair 20cm sections of deflector magnet during operation, if they are submerged in a liquid helium bath. Lastly, the small field irregularities at rotor joints will result in losses proportional to B2, meaning we may have 64 times as much loss and control voltage fluctuation with these high field magnets.

Higher accelerations result in shorter perturbation wavelengths - not a lot shorter, granted. As I recall, 4x the acceleration scales to half the wavelength, given the same stiffness. But the controller and section length must be reduced. At some point, the geometries become impractical, with coils that are too short longitudinally, with too much edge effect between coil segments.

I prefer plain old transformer steel laminations, and plain old copper wire. The ambits get bigger, but the total deflection force and the total amount of structural material is the same. Cooling is spread out, control systems are spread out, and the possibility of catastrophic failure is much reduced. If copper and steel are too expensive, superconductors will not be any cheaper.

Here is a graph of saturation B field versus H field for common ferromagnetic materials, at room temperature. The graph is taken from the Wikipedia article Saturation (magnetic), and from figure 42 of Theory and Calculation of Electric Circuits by Steinmetz, Charles (1917), McGraw-Hill, with additional notations added and some lines representing multiples of the vacuum permeability. Click the drawing for higher resolution.

Option B: Pure soft iron saturates at 2 Tesla. Hiperco 50A (almost 50% cobalt and very expensive! from Carpenter Specialty Alloys) saturates at 2.4 Tesla with a magnetization of 0.5 Oersted (about 40 A/m). Laminations made from these materials may be suitable for rotor and deflection magnets. The deflection magnets might have an additional "edge winding" designed to switch quickly for faster control.

AmbitMagnets (last edited 2017-05-31 18:32:16 by KeithLofstrom)