Limitations for velocity of projectile are investigated for a multistage reluctance accelerator having identical coils. Geometrical parameters of winding are used as basis, assuming an overdamped system fed from large common capacitance.

Limitations layed by ohmic heat and weight of capacitor were taken into account. Red-colored cells of the tables correspond to the capacitor mass exceeding a resonable limit. Range of values for which no overheat occurs, is covered with green color.

Generally, we can see that both limits under concern work in one direction, constraining vmax for accelerators with thin long windings. "Heat" limit plays major role for the small calibers. At 8 mm bore the borders for the limits coincide, and for 12 and 20 mm bores "green zone" covers all the tables, and only "mass limit" manifests.

Other limiting factors like wight of the coils can also be taken into account by a similar way.

Conclusions and discussion.

Following conclusions can be made.

1) On the assumption of the geometrical properties of multistage accelerators with identical coils, theoretical velocities of 100..130 m/s are achievable for the calibers of less than 8 mm. The highest-speed caliber is about 5 mm.

2) The obstacles on the way to higher speeds are overheat of the coils for small-bore coilguns, and huge mass of the power capacitor for large-bore ones. For 20 mm and larger calibers velocities of more than 70 m/s cannot be obtained exclusively because of geometry of the coils (even without the "weight" limitation).

3) vmax falls with coil's thickness growth and length decrease. The thickness is more critical - the velocity decreases by an order of magnitude when the outer diameter grows from 1,1·d to 2·d, and only triply when relative length increases from d to 4·d.



It is clear that small calibers are the most attractive for breakthrough to high velocities. They are even more tempting if we note that mass is not the only reason which limits us in a portable system - the length acts, too. 16 stages of 12 mm gaussgun with l/d = 4 ratio would make 80..90 cm in total (assuming some additional place for detectors and other elements of the construction) - this is a bit excessively. For 3 mm-bore coilgun total length would be 20..30 cm only.

The first table says that supersonic velocities can be obtained theoretically. Сooiling of windings with liquid nitrogen or Peltier modules can be used prior to shot to prevent overheat (such a method was proposed by many authors for induction launchers). In this case, the efficiency would increase not only because of active resistance reduction, but also because of the speed growth (see here).

As for large caliber coilguns (more 10 mm) with identical windings, the results above make us claim that velocities of projectile of more than 100 m/s cannot be obtained with state-of-art electronics (unless some tricky technologies are utilized like recuperation).

To Sulaiman:

For a still fairly simple analysis why not maintain coil geometry
but use thinner wire at the start with the wire getting appropriately* thicker/more strands for successive stages.

May be I'll try such an analysis later. The problem is that inductance varies vary fast with wire gauge d (in inverse proporion to (d in 4th power).
Anyway, the identity of the stages is lost here.