How can I calculate the temporal characteristics of a pulsed solenoid circuit?

[lichen]

Hello!

I wonder if anyone can give me some quick advice.

I'm designing a physically small (but high current) pulsed solenoid. The circuit will basically be an RLC circuit where a switch is thrown to discharge the capacitor into the coil, giving a strong short-lived magnetic field.

I'm doing all right with the design so far, but I am having trouble getting an idea of the temporal characteristics of the pulse - i.e. how the current through the solenoid will increase then decrease over time. I know that roughly speaking it will have a growth period defined by the initial inductive resistance to current, followed by a decay.

Can anyone mathematically quantify the time situation here for me, in terms of R, L, and C? The R may be a small resistor in the circuit, or it may simply be the wires/coil resistance - shouldn't matter.

Many thanks.

- Lichen

 

[pzlded]

Hi Lichen,

I assume you have given due consideration to the usual design requirements. For example, minimizing electrical resistance has the following potential benefits - faster response, good thermal efficiency, lower operational cost, reduced applied voltage requirements (increased mechanical force per applied volts), increased pulse frequency limit, reduced weight, increased reliability, improved consistency of response among multiple solenoids, and increased tolerance of environmental factors. For high frequency, there might be a benefit to minimizing persistence of magnetism in the core.

I'm doing all right with the design so far, but I am having trouble getting an idea of the temporal characteristics of the pulse - i.e. how the current through the solenoid will increase then decrease over time. I know that roughly speaking it will have a growth period defined by the initial inductive resistance to current, followed by a decay.

The following URL (Wikipedia) provides some basic equations.
http://en.wikipedia.org/wiki/RLC_circuit

Concerning the temporal characteristics:
1. When volts are first applied, magnetic energy within an inductor is increases the fastest, because voltage applied to the inductor is maximum.

$$V_{L} = L\frac{\partial I}{\partial t}$$

2. Current takes time to increase. Initially inductor volts = source volts, because resistor volts = zero, because current = zero.

3. As current increases, volts through the resistor increase, reducing the rate current and magnetic energy increases. When resistor volts nearly equal source volts, inductor volts nearly equal zero, thus current will cease to increase.

4. If resistance = zero, constant volts applied to an inductor will eventually cause infinite magnetism and current (in theory). In other words, high applied volts plus low resistance, maximizes the rate magnetic energy increases.

 

[lichen]

Thanks.

The solenoid will be air-core because I need to produce a very high strength pulsed field (5T). I will probably need some form of cooling, and I have been recommended that a good idea is to use microbore copper tube (of electrical grade copper) which I will shrink wrap. This will form the coil winding but also have water run through it to cool it. So, what I'm really saying is, I have thought about the resistance, and I'm trying my best to lower it.

The situation will be a capacitor is fully charged then a switch is thrown and it is allowed to discharge into a coil. I understand the theory you talked about pzlded, but what I'm really looking for is a calculation of the time characteristics of the current pulse, in terms of R, L and C.

 

[pzlded]

Hi Lichen,

The solenoid will be air-core because I need to produce a very high strength pulsed field (5T). I will probably need some form of cooling, and I have been recommended that a good idea is to use microbore copper tube (of electrical grade copper) which I will shrink wrap. This will form the coil winding but also have water run through it to cool it. So, what I'm really saying is, I have thought about the resistance, and I'm trying my best to lower it.

Pulsed solenoids are outside my area of expertise; the following is my ‘opinion’.
I am surprised about your use of heat shrink-wrap on a potentially high temperature magnet. I also thought you would want a high density of coils (square wire windings with high temperature insulation + external water-cooling (based on rate of heat production)) to produce ‘concentrated magnetism’. Microbore copper tubing is not very compact. Perhaps it is possible that one of the magnet wire manufacturers has some specification data.
http://www.mwswire.com/

The complete conversion of a large quantity of voltage’s energy to magnetic energy is never instantaneous (not even with a superconductor connected to a supercapacitor); there is always a non-ideal rate of conversion, dependent on the specific type of circuit components.

 

[lichen]

The shrink-wrap-to-insulate method was recommended to me by a Professor who uses it in his group's own solenoids, as was the microbore tube method. It is an efficient way to water-cool the solenoid (the only alternative is to encase the whole structure in aluminium and have water rushing around the whole device - you can imagine how much more complex this would be to construct and also heat cannot readily escape into the water since at such high fields the whole coil has to be embedded in epoxy for strength).

If I am correct (I hope so) I should be able to purchase microbore electrical grade copper tube with an outer diameter of down to something like 0.5 mm.

I'm using Qucs just now to simulate the situation, and the transient current and resultant field both look correct.

I will probably need to apply some sort of non-linear crowbar device to the circuit to limit the pulse to one half-sine and then a discharge to earth, as it looks like it will tend to oscillate due to the LC which will cause un-needed heating and may damage the capacitor...

I'll let you know how I get on anyway.

 

[pzlded]

I think that it is extremely difficult to build a durable non-superconductive 5T magnet

Albeit the following would not produce a pulsed magnetic field, perhaps it is possible to modify an existing superconductive magnet, to produce a square wave of magnetic energy. Commercial 5T superconductive magnets exist and (small) efficient commercial superconductive transformers exist. Superconductive magnets are charged by applying volts to a small segment of wire heated above critical temperature, while the rest of the magnet is superconductive. As long as volts are applied, magnetic energy increases. When the segment is cooled to critical temperature, the magnet efficiently stores magnetic energy.

Magnetic polarity change losses might be trivial. When an open circuit transformer reverses magnetic field, the open circuit holds little voltage’s energy and the transformer itself usually has low thermal loss. The following URL provides some general info on superconductivity within atoms and semiconductor material plus other general info about magnetism and voltage.
http://mysite.verizon.net/richarddesaneis/