Mass Drivers

Coil Guns aka Mass Drivers probably are too expensive, due to the high cost of high voltage switching electronics near the breech (output) end. The scaling cost goes proportionally to the mass and to the cube of the breech velocity, as we shall see.

For lowest cost, assume a resonant/wasteful mass driver without energy recovery, driving similar payloads to similar velocities. While this is restrictive, it means that one switch (the expensive part) can drive many resonant coils from one AC capacitor.

This is wasteful because all coils but the one immediately driving the payload will be radiating energy. Also, the amount of energy in the section will diminish as the payload passes, so the energy transfer will be uneven over a section. A "single switch and capacitor per coil" system is much more flexible, but the additional switching electronics greatly increases the cost.

General note on electronics and reliability

"Cheap, fast, good - pick two" old electronics adage.

Any system incorporating kilometers of electronics must be made with highly reliable components used in highly reliable ways. If the system is dependent on millions of assemblies containing hundreds of components each, working for many years, then each component must have a mean failure rate of less than a part per trillion per hour. No such components exist. Even with redundancy, fail-safes, and careful design for uncorrelated failure modes, a multi-year lifetime is difficult to achieve.

Heat is the enemy of reliability. The failure rate of components typically doubles with every 10C temperature increase. The failure rate also tends to follow a "bathtub curve", with high initial failure rates, a few years of moderate rates, followed by high "wear-out" rates near the end of life. Most wear-out mechanisms are related to mechanical stress, impurity infiltration, and material migration, particularly where currents or voltages or temperature gradients are high.

In consumer electronics, there is such a thing as "too much reliability". Henry Ford was reputed to comb the junk yards, looking at broken Model T's. He was looking for components that were not broken or worn out. The pinion arms in the steering system were always intact, implying that they used too much expensive steel and weighed too much, so he told his engineers to make them lighter. The result of thousands of decisions like that resulted in a less expensive car. Modern electronics is designed to last a fairly long time, on average, to reduce the number of expensive warranty returns. If you want to replace less than 0.1% of your cell phones during a one year warranty period, you might have to design most components to last 10 years, with an average one year failure rate of one part per million. However, components with low "bathtub" rates, which reliably last 3 years but suffer from wearout in five, are just fine for 1 year warranty products. Electrolytic capacitors and microprocessor sockets are examples of this kind of component. If you spend more on materials, you will typically make assemblies larger, increase price, and reduce the performance. Given that most consumers replace old models for new models more frequently than the components wear out (creating more sales opportunities) there is strong counter-incentives to maximize reliability.

Indeed, decreasing reliability is often mandated by law. RoHS lead-free solder has a high tin content, and tin crystals have the unfortunate tendency to relieve stress by growing filaments of tin out of the side of solder joints. These whiskers short across the small insulating gaps in miniaturized electronics. These solders melt at higher temperatures, so there is more built-in stress when they cool. If the electronic system handles a lot of power, or pulse power, the temperature cycles can severely aggravate whisker formation.

This is what high-volume, Consumer-Off-The-Shelf (COTS) electronics is geared for. That makes these inexpensive and well characterized components risky to use for military, space, and medical applications. On the other hand, the very low production volumes associated with these high-reliability markets leads to poor characterization, which itself is a source of low reliability. Perhaps the best match for high-reliability markets is automotive-grade parts. For safety reasons, these parts need to be high reliability, and the volumes are adequate to increase scrutiny and lower cost. The mediocre track record of automotive electronics suggests it will be a while before these components live up to their potential.

Semiconductor Reliability

Inside power electronic chips, semiconductors are very poor heat conductors. Mono-isotope diamond/carbon has the best heat conduction of any semiconductor, but we still don't know how to make useful transistors with it, and even diamond has poor heat conduction compared to metals. Graphene will work much better, but we don't know how to reliably fabricate that. Among production-ready materials, silicon still reigns. Exotic 3-5 compounds like Gallium Arsenide have poor heat conduction, and insulators are worse. So, assume silicon for bulk power handling - 99%+ of all power electronics uses silicon power components.

Semiconductor chips use mostly surface phenomena. Chips are usually more than 100 microns thick, but the active area is within a few microns of the surface. The rest of the thickness is there for mechanical handling during manufacturing. The active transistors are built within the silicon. Above the silicon are layers of glass and metal. Heat propagates through the silicon by diffusion, the way warm air diffuses into the room. Mechanical shock moves through the silicon at the speed of sound - 8400 meters per second, or 8.4 micrometers per nanosecond. Heat diffuses more slowly than sound. As a result, the surface of the silicon can be a lot hotter than the metal heat sink underneath. On the surface itself, there are hot spots. And the overlying glass and metal have different thermal coefficients of expansion than silicon. So, when silicon is subjected to pulse power, it undergoes a lot of stress, potentially cracking insulators and shearing metal, with thermal gradients pushing contaminants into the silicon and damaging the transistors.

Very high speed pulses, on the order of nanoseconds, will dump a large heat load into the surface of the silicon, which will thermalize and heat that surface area a lot . The diffusion time to the bottom of the silicon will be slower, approximately proportional to ( 1.65E6 J/m3-K / 149 W/m-K ) times the thickness squared, about 100 microseconds for 100 micron thick silicon. Looked at differently, a 10 microsecond pulse will heat the top 30 microns of silicon, resulting a heat capacity of 5 mJ/cm2-K. If the 10 microsecond heat pulse is due to ohmic heating, and the electrical resistance of a 1 cm2 switch is 50 m\Omega , then a 1000 amp pulse will dump 50KW for 10 microseconds or 50 millijoules into the silicon surface, resulting in a very quick temperature rise of 10 Kelvins. If the transistor is rated at 200V, and making 100V pulses, the pulse energy will be on the order of one Joule.

MORE LATER

Capacitors

All capacitors are not created equal. Real capacitors have series inductance, series resistance, and leakage resistance. "Supercapacitors" tend to have very high Equivalent Series Resistance (ESR) with time constants on the order of 10 to 100 milliseconds, see http://avx.com/docs/Catalogs/bestcap.pdf. They also leak, with a leakage time constant of on the order of 10 hours at room temperature, decreasing rapidly as the capacitor heats up. Since a sizable portion of the energy ends up in the series resistance, they will heat up. Supercapacitors are best suited for electric cars, providing extra startup current for stalled motors, and for storing the energy from regenerative braking, until batteries have time to interact. These low-speed operations match what supercapacitors can do.

Higher voltage capacitors have much less capacitance. The { \small { 1 \over 2 } } C V ^2 per volume is pretty much the same for a given dielectric, so if V doubles, we can expect C to be reduced by a factor of 4.

Capacitors have other quirks. Most are piezoelectric - charging them causes them to deform mechanically. Inductive currents from rapid discharge create magnetic fields and forces as well. If the capacitor is not designed for rapid discharge, it can explode. For example, high voltage, 60Hz line correction capacitors sometimes appear on the surplus market. Some hobbyists use these to build electromagnetic coin crushers. These re-purposed capacitors are usually good for less than 1000 shots before they explode (inside a metal box, inside concrete, in another room, please).

So where high voltage fast pulses are needed, any old capacitor will not do. Low ESR, low inductance, mechanically reinforced capacitors must be used, the kind used in pulse lasers and magnetic electroforming equipment. MORE LATER