FUTURE POWER SUPPLIES AND ELECTRICAL WEAPONS - From impracticality to superiority without exceeding the energy density of TNT!

I'm working on a future history project spanning the next thousand years, and I've had an interesting time working out the power supplies that will allow laser pistols and gauss rifles to eventually replace old style chemical slugthrowers. I wish to share my work for other writers who want to make their futuristic weapons a bit more realistic, or at least consistent. If my maths is wrong feel free to correct me.

Modern power supplies are useless for the task - our capacitors dont provide enough joules and our batteries dont provide enough watts. Future power supplies may be able to solve this, but Routledge's Law claims that "Any interesting battery material for a laser gun would be more usefully deployed as an explosive warhead." I think that is based on the misconception that laser efficiency cannot improve beyond the present and that their only damage mechanism can be as a brute force "heat ray". 

If Dr John Schilling and Dr Luke Campbell of Atomic Rockets are correct about the mechanical effect of ultrafast pulses and if i have done my maths right (seriously i am terrible at maths so perhaps i am totally wrong), then high energy gauss and laser weapons may achieve the ammo-to-mass ratio needed to render chemical slugthrowers obsolete without the energy density of batteries matching the energy density of chemical explosives (5000J/g). 

First, some hypothetical power supplies. We will assume that our future weapons have an internal capacitor which is recharged by an external battery (not necessarily traditional electrolytic capacitors and chemical batteries, they could be some advanced nanotech ultracapacitors optimised for different purposes, who knows):

Present day (21st century)  

Capacitor - 1J/g - 100W/g  

Battery - 360J/g - 1W/g

Near future (22nd century)  

Capacitor - 10J/g - 400W/g  

Battery - 500J/g - 5W/g

Mid future (26th century)  

Capacitor: 25J/g - 1000W/g  

Battery: 1000J/g - 10W/g

Far future (28th century)  

Capacitor: 50J/g - 1500W/g  

Battery: 2000J/g - 15W/g

Now some future weapon efficiencies (to keep things simple, battery efficiency remains constant) of hypothetical electrically powered weapons.

1kJ output at 20-25% efficiency  

4kJ capacitor drain  

4.8kJ battery drain

1kJ output at 27-33% efficiency  

3kJ capacitor drain  

3.6kJ battery drain

1kJ output at 41-50% efficient  

2kJ capacitor drain  

2.4kJ battery drain

1kJ output at 55-66% efficiency  

1.5kJ capacitor drain  

1.8kJ battery drain

1kJ output at 69-83% efficient  

1.2kJ capacitor drain  

1.44kJ battery drain  

I really hate this next bit cos i am terrible at maths, but i think what we do is we multiply the energy drain by the number of shots we want in that stage to find how much energy we require, (i.e. if a mid-future 1kJ laser gun drains 2kJ at the capacitor, then a 5-shot capacitor needs to hold 10kJ), then we take the energy requirement and divide (or was it multiply?) it by the energy density of the power supply (i.e. 10kJ required divided by 0.025kJ/g energy density = 400g) to find the size of your capacitor or battery.

Some finished examples:

Present day  

20-25% efficient 1kJ laser

1shot capacitor: 4kg (4kJ, 40kW)

100shot battery: 1334g (480kJ, 1.3kW)

27-33% efficient 1kJ gauss  

1shot capacitor: 3kg (3kJ, 30kW)  

100shot battery: 1kg (360kJ, 1kW)

Near future  

27-33% efficient 1kJ laser  

3shot capacitor: 900g (9kJ, 360kW)  

250shot battery: 1800g (900kJ, 9kW)

41-50% efficient 1kJ gauss  

3shot capacitor: 600g (6kJ, 240kW)  

250shot battery: 1200g  (600kJ, 6kW)

Mid future  

41-50% efficient 1kJ laser  

5shot capacitor: 400g (10kJ, 400kW)  

500shot battery: 1200g  (1.2MJ, 12kW)

55-66% efficient 1kJ gauss  

5shot capacitor: 300g (7.5kJ, 300kW)  

500shot battery: 900g  (900kJ, 9kW)   

Far future  

55-66% efficient 1kJ laser  

10shot capacitor: 300g (15kJ, 450kW)  

1000shot battery: 900g  (1.8MJ, 13.5kW)

69-83% efficient 1kJ gauss  

10shot capacitor: 240grams  (12kJ, 360kW)  

1000shot battery: 720grams (1.44MJ, 10.8kW)

Links and resources:

The place that got me started:  

http://www.projectrho.com/public_html/rocket/sidearmenergy.php  

http://www.projectrho.com/public_html/rocket/sidearmslug.php

Some useful calculators:  https://www.omnicalculator.com/physics/efficiency  

https://www.omnicalculator.com/physics/work-and-power  

You'll need this to figure out how heavy/fast your gauss gun slugs need to be:  

https://www.calculatorsoup.com/calculators/physics/kinetic.php

Dr Luke Campbell's calculator will help you figure out how much damage a laser can do:  

http://panoptesv.com/SciFi/LaserDeathRay/DamageFromLaser.php

Electrical engineer Barry Hansen's website is chock full of technical information for practical coilgun design:  

https://www.coilgun.info/about/home.htm

Use this to help you figure out how small the spot size of your laser is with a given aperture size and distance:  

https://www.lasercalculator.com/laser-spot-size-calculator/

Effects of Directed Energy Weapons - a technical guide covering lasers, masers, particle beams, railguns and coilguns:  

https://www.hsdl.org/?view&did=440713

Basics of Electric Weapons and Pulsed-Power Technologies:  

https://apps.dtic.mil/sti/pdfs/ADA557759.pdf

Some patents for handheld laser weapons:  

https://patents.google.com/patent/US9303958B2/en (25% efficiency!)  

https://patents.google.com/patent/US20030233931A1/en  

https://patents.google.com/patent/US8322263B2/en (that last one uses gas cartridges, very cool)

A patent for spin-stabilisation of electromagnetically propelled projectile (so your gauss rifle can be a real rifle!):  

https://patents.google.com/patent/US4449441A/en

And finally, a look at lasers in the near future:  

https://spaceanddefense.io/laser-pistols-emerging-weapon-and-tactics/