Could a photonic engine actually work?

Question

I have a very specific aesthetic in mind for my science-fantasy setting, technology is largely pneumatipunk supplemented with weired phonotic devices;for "reason" there are few electrical devices in use. An engine that uses focused light for thrust fits my aesthetic perfectly.

However I was wondering if a photonic thruster would actually work?

Why?

Because I'd rather not "handwave" if a real world solution actually exists.

Ion propulsion works , thus we've got proof of particle thrust, the question is could something similar be done with photons. If not photons, what if light was focused into something more substantial would that put a photon thrust in the realm of plasma thruster.

Answer 1

TL;DR - Not practical due to high energy demands

Lets examine the power of a photonic thruster using two wavelengths, one long (radio/UHF at 3 Ghz, 0.1 meter wavelength) and one short (x-rays at 300PHz, 1nm wavelength). The energy of a photon ($E$) is defined by $E = \frac{hc}{\lambda}$ while the momentum ($p$) is $p = \frac{E}{c} = \frac{h}{\lambda}$. $h$ is Plank's constant $6.626\times10^{-34} \text{J}\cdot\text{s}$, and $c$ is the speed of light $3.00\times10^8\frac{\text{m}}{\text{s}}$.

For a 1.0nm photon, $E = 2.0\times10^{-16}\text{J}$ and $p = 6.6\times10^{-25}\frac{\text{kg}\cdot\text{m}}{\text{s}}$.

Lets compare a theoretical x-ray photonic engine with a Hall effect thruster (which have flown in space since the 70s).

A generic hall effect thruster requires input power of 2kW and generates thrust of 100 millinewtons. Assuming a 1000kg satellite, acceleration will be $a = \frac{F}{m} = \frac{.1\text{N}}{1000\text{kg}}=0.0001\frac{\text{m}}{\text{s}^2}$. Therefore in 1 day (86400s) of thrusting it can take a 1000kg satellite from rest to a speed of $v_f = v_i + a\cdot t = 0 + 0.0001\frac{\text{m}}{\text{s}^2}\cdot 86400s = 8.64 \frac{\text{m}}{\text{s}}$. Not too much acceleration, but it only took 2kW of power.

Now lets try to get our photonic propulsor to match that speed. The momentum change required for a 1000kg satellite to 8.64 $\frac{\text{m}}{\text{s}}$ is 8640 $\frac{\text{kg}\cdot\text{m}}{\text{s}}$. If each photon's departure from the engine imparts $6.6\times10^{-25}\frac{\text{kg}\cdot\text{m}}{\text{s}}$, then $n = \frac{8640 \frac{\text{kg}\cdot\text{m}}{\text{s}}}{6.6\times10^{-25}\frac{\text{kg}\cdot\text{m}}{\text{s}}} = 1.30\times10^{28}$ photons are needed, requiring an energy of $ 1.30\times10^{28} \cdot 2.0\times10^{-16}\text{J} = 2.59\times10^{12}\text{J} $. Divided by a day, that works out to 30 MW just for the energy that need to be imparted to the photons, assuming a perfectly efficient engine.

So there you see the problem. A photonic thruster will require (at perfect efficiency) about 4 orders of magnitude more energy than a current technology ion thruster to generate the same thrust. I would assume that future ion engines will be even more efficient. Also notice, that the ratio between momentum and energy in a photon is constant (the speed of light) so the theoretical max efficiency of the thruster does not change with wavelength.

So a photonic thruster is not practical with real physics; this explains why photon related thrust proposals involve solar sails, where the sun is giving the photons the energy.

If you want to use 'maybe' physics, then you could say that there exists a way to generate photons that does not require energy generation in the form of electricity. Some exotic interaction of dark matter/dark energy/anti-matter etc. Or you could just say its magic. In that case the photonic thruster would work, but watch out for whatever you are pointing that thruster at. If the photons pack 30MW at 100 mN, then they will be worth 39TW if they match the 130kN of an F-15's twin engines. That is more of a death ray than a transportation system.

Answer 2

Photonic engine like you have described would work. After all, photons have pushing power and if pushing is involved, there would be recoil.

There are two issues with this engine: like ion drive, photon drive will also be a high impulse propulsion and you will need an alternative way to achieve orbit first.

Second problem is that the recoil of light is very very very small. I am not a physicist so correct me if I am wrong, to calculate the push of the light we need to convert the energy contained in that light to mass equivalent times its speed. As the photons has no mass at all so pushing power of it comes from its energy. So lets say energy of photons is $E$. To get mass, we need to divide it by $c^2$ from $e = m c^2$. If we multiply that by its speed $c$, the resulting formula would be $\frac{E}{c}$ which does not look very good. Lets say you have 3 MW ( = $3 \times 10^6 kg.m^2/s^3$) laser. Divided by $3 \times 10^8 m/s$ will give us $0.01kg . m / s^2$ push. This will accelerate a 1 ton spacecraft by $3.2 km/h$ every day. But mind you, a 1 MW diesel generator weighs 5 tons without fuel. I don't believe this is efficient enough. Probably, ion propulsion would do much better and it is much simpler.