Storing Megajoules to Spend Them in Nanoseconds
Pulsed power is the art of collecting energy slowly and releasing it all at once. A capacitor bank charges over minutes from an ordinary supply, then dumps its entire contents in a time short enough that the instantaneous power dwarfs anything the grid could deliver. The megajoule is the unit the bank is sized in; the joule is the unit the individual shot, the individual capacitor and the peak-power division are written in. Moving between them is the routine arithmetic behind every ignition campaign, every railgun test and every capacitor-discharge machine on a lab bench.
What Sets the Number on Both Sides of the Field Pair
Half C V Squared Sets the Bank Size
Stored Is Never Delivered
Energy Divided by Time Is the Whole Point
A Bank Stays Charged After the Supply Is Off
From Bank Capacitance to a Peak-Power Figure
The useful sequence runs capacitance and voltage into joules, joules into megajoules for the specification sheet, and joules divided by pulse length into watts. Keeping the joule figure in front of you the whole time is what makes the last step painless.
Work out the stored energy first
Evaluate ½CV² with capacitance in farads and voltage in volts, and the answer is already in joules. A 200 µF defibrillator capacitor at 1 900 V gives 0.5 × 0.0002 × 1 900² = 361 J.
Lead with whichever unit your source printed
Facility documents quote megajoules, component datasheets quote joules. The swap arrows put either one on the input side, and both boxes stay live, so a bank rating and a single-capacitor rating can be checked against each other without retyping.
Divide the joules by the pulse length
1.8 MJ is 1 800 000 J; delivered over a 20 ns window that is 1 800 000 ÷ 2 × 10-8 = 9 × 1013 W, which is 90 TW averaged across the pulse.
Carry the joule value into the power division
The copy control above each field returns the digits alone, with no unit and no thousands spacing, which keeps a seven-figure joule value clean for the spreadsheet cell that will divide it by a nanosecond pulse width. Ctrl+C in a field behaves identically.
Pulsed-Power Machines by Stored Energy and Pulse Length
Each row gives the energy in both units, the rough duration over which it is released, and the power that division implies. The range runs from a photographic flash to an inertial-confinement facility, and every entry is the same arithmetic applied at a different scale.
| Device or shot | Energy (MJ) | Energy (J) | Pulse | Power |
|---|---|---|---|---|
| Xenon camera flash | 0.00005 | 50 | 1 ms | 50 kW |
| Defibrillator shock, maximum setting | 0.00036 | 360 | 10 ms | 36 kW |
| Capacitor-discharge spot welder | 0.005 | 5 000 | 10 ms | 500 kW |
| Laboratory bank, 1 mF at 20 kV | 0.2 | 200 000 | 100 µs | 2 GW |
| Electromagnetic launcher shot | 32 | 3.2e+7 | 10 ms | 3.2 GW |
| Z-pinch machine, X-ray output | 2.7 | 2 700 000 | 8 ns | 337 TW |
| Z-pinch machine, stored in the Marx bank | 20 | 2.0e+7 | — | — |
| Ignition-class laser, energy on target | 1.8 | 1 800 000 | 20 ns | 90 TW |
| Ignition-class laser, capacitor bank stored | 400 | 4.0e+8 | — | — |
Two comparisons carry the table. The launcher and the Z-pinch X-ray burst hold energies within an order of magnitude of each other, yet their peak powers differ by a factor of about a hundred thousand purely because one pulse is milliseconds and the other nanoseconds. And the last two rows show the storage penalty: 400 MJ goes into the bank so that 1.8 MJ arrives at the target, an end-to-end efficiency of roughly 0.45 per cent.
What the Field Pair Contributes to a Shot Calculation
Stored and Delivered Energy Without Rescaling
A 400 MJ bank and a 1.8 MJ shot differ by more than two orders of magnitude, and both land in the same field pair as plain readable digits rather than exponents.
Sub-Joule Pulses Keep Their Decimals
Trigger circuits and individual Marx stages often sit well under a joule. Eight decimal places are printed before exponent notation takes over, so a millijoule stage does not collapse to zero megajoules.
Plain Joules for a Peak-Power Divide
Copying strips the unit and the thousands spacing, so the joule figure pastes straight into the division by pulse width that produces a terawatt number.
Enter a Shot Energy Already Logged in Joules
Diagnostics log in joules while campaign summaries report megajoules; the arrows reverse the pair so whichever record is in front of you becomes the input side.
Questions From the Capacitor Room and the Shot Log
How does ½CV² turn capacitance and voltage into a bank rating?
Charge accumulates in proportion to voltage, so the work done pushing it in integrates to half the product of capacitance and voltage squared, in joules when C is in farads and V in volts. A 1 mF unit at 20 kV therefore stores 200 000 J, or 0.2 MJ. The squared term dominates every design decision: keep the same 1 mF but charge to 40 kV and the store rises to 800 000 J, four times as much from identical hardware. It also means a bank charged to only half its rated voltage is holding a quarter of its rated joules, not a half.
Why does a 400 MJ bank put only 1.8 MJ on target?
Because a laser chain is a sequence of lossy conversions. The bank fires flashlamps, the lamps pump amplifier glass, the glass gives up a modest fraction of that as infrared light, and frequency conversion to the ultraviolet takes another substantial cut before anything reaches a target chamber. Four hundred megajoules is 4.0 × 108 J and 1.8 MJ is 1 800 000 J, so the whole chain runs at about 0.45 per cent. That is not a design failure — the point of the machine is concentration in time and space, not electrical thrift.
How do a few megajoules become hundreds of terawatts?
Entirely by compressing the time axis. Power is energy divided by duration, so 2.7 MJ — 2 700 000 J — released across 8 ns gives 2 700 000 ÷ 8 × 10-9 = 3.375 × 1014 W, about 337 TW. For a few nanoseconds that exceeds the entire electrical generating capacity of the planet, which sounds impossible until you notice the energy involved would run a domestic kettle for roughly twenty minutes. Pulsed power buys instantaneous power, never total energy.
What does target gain mean when a shot returns more than it received?
Target gain compares the fusion energy out with the laser energy delivered to the capsule — nothing else. A shot taking in 2.05 MJ (2 050 000 J) and yielding 3.15 MJ (3 150 000 J) has a gain of about 1.54. Set against the bank that charged the lasers, however, the same shot consumed hundreds of megajoules, so the wall-plug balance stays deeply negative. Both statements are true simultaneously, and confusing the two is the single most common misreading of an ignition result.
Why is a bank treated as live long after the supply is off?
Because a capacitor does not need a source to remain charged, and dielectric absorption can push voltage back onto plates that were shorted only briefly — the so-called soakage or recovery effect. A 100 µF unit resting at 5 kV still holds 1 250 J, more than three times a maximum defibrillator discharge and far above the tens of joules considered lethal across the chest. Standing procedure is a dump resistor, then a grounding stick left in place, then measurement — and never a shortcut on the grounds that the shot already fired.
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