Mass Drivers

work in progress - more will be added later

Coil Guns aka Mass Drivers are probably 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.

Many approximations follow, in order to arrive at a rough order of magnitude. Note that magnetic fields do not always go where we want them to - directing them usually involves channels of ferromagnetic material, which typically is pretty dense and heavy. The assumptions below are probably VERY optimistic.

Assume the target mass driver accelerates a 100kg payload at 1000 m/s2 to 10,000 m/s . The acceleration length is 50 km, V^2/2*a . If the vehicle is pulled by a string of 10 each 5cm magnets, then each magnet will be experiencing a force of 10,000 Newtons over a surface area of 5cm*5cm, for a force density of 4E6 Pascals . This force represents an energy density of 4E6 J/m3. Assuming this energy (as a magnetic field) fills a volume of 10cm cubed, then the energy is 4E3J. As the payload travels along, volumes are filled then depleted of energy in the time a payload travels 5cm, so the energy pulse width is on the order of 5cm / 1E6 cm/s or 5 microseconds.

Note that larger magnets can have slower gradients, but a correspondingly larger volume of space must be filled and depleted with energy as the payload passes. So, doubling all the dimensions results in 1/4 of the pressure, 1/4 of the energy density, 8 times the volume, twice the energy, twice the pulse time, same switched power level.

If the energy ramps from 0 to 4E3 J in 5 microseconds, then back to zero in 5 more microseconds, then for the first part of the pulse, the power level is 800 megawatts feeding in, followed by 800 megawatts draining back out. Not quite - in 5 microseconds, the vehicle moves 5 cm, with a force of 10,000 Newtons per magnet, and pulls 500 Joules out of the energy field. The "drain" pulse is "only" 700 megawatts per magnet, 7GW total for all the magnets.

This power is switched by some kind of controllable electronic switch. It could be a gas discharge tube, and thyristor, or a power MOSFET. Of those, only a power MOSFET switches fast enough, with microsecond pulse timing accuracy. The MOSFET must be able to stand off the highest voltages encountered while not conducting (Breakdown voltage) while passing the currents involved without heating up too much. MOSFET thickness must go up and the doping gos

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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". 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 need 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 three years but suffer from wear-out in five, are just fine for 1 year warranty products. Electrolytic capacitors and microprocessor sockets are examples of this kind of component. If you increase material weight, you will often make assemblies larger, increase price, and reduce performance. Given that most consumers replace old models with higher performance new models more frequently than the components wear out, creating more sales opportunities, there are strong counter-incentives to maximize reliability beyond warranty demands.

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 filaments short across the small insulating gaps in miniaturized electronics. Low-lead solders melt at higher temperatures, so there is more built-in stress when they cool. If an 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, while their 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.

The most popular semiconductor switch is the power MOSFET. Unlike planar silicon, these devices use the whole depth of the die as a drift region, to stand off higher voltages. The drift region must be thick enough and lightly doped enough to reduce the maximum electric field. However, a thicker die and lower doping also increases the turn-on resistance, proportional to the 2.5 power of the breakdown voltage V_B .

How thick? How much resistance? Let:

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See http://en.wikipedia.org/wiki/Power_MOSFET and "A Parametric Study of Power MOSFETS" by Chenming Hu, IEEE Power Electronics Specialist Conference, 1979 pp 385-395.

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