Anti-Orbit Laser Submarines

Laser-equipped nuclear-powered submarines are the perfect last line of defense against an attacking force in orbit.

The situation

You don't win every fight. Eventually, there will come a time in space warfare where a fleet of space warships has defeated all your mobile forces and your immobile defenses. They will bear down on you from above with lasers, missiles and kinetic projectiles and you will have to find a way to prevent their forcing of an unconditional surrender. 

We will refer to the opponents as the 'attackers' and to you as the 'defenders'. The first step to devising an effective defense is to understand the situation.

So what is the situation?

Its an enemy ship.

An attacking warship will start out in high orbit. This is an altitude of 2000km or above. Whether it has just arrived from an interplanetary voyage or has recently destroyed your remaining warships, it will go to high orbit to maximize the effectiveness of its space superiority. Space superiority, borrowing from the term 'air superiority', is when a force has complete dominance over all the orbits around a planet. No space-borne forces can oppose this superiority and no reserve forces can challenge them without being quickly destroyed. 

What does losing space superiority mean for defenders?

The most important consequence is that enemy warships have free reign to change orbits, maneuver into favorable positions and receive re-supplies. Their mobility is unconstrained. 

High Elliptic Orbits and gravity assists from a large moon allow for a huge variety of orbits.

Attackers in high orbit can make optimal use of their laser weaponry. They can get clear lines of sight onto any spot on the surface, and the long distances between objects forces travel times to lengthen with the secondary effect of giving lasers plenty of time to shoot down targets. Laser effectiveness is generally dependent on how far they are from a target and how much 'dwell time' a beam can spend on a target. 

De-orbiting objects from high altitude is inexpensive in terms of deltaV. This works in favour of missiles sent down from orbit by allowing them to use very little propellant to strike ground targets, which makes them lightweight and cheap to send by the hundreds. Additionally, falling towards Earth gives them a big boost to the velocities they achieve before impact. 

The same applies to kinetic projectiles, a fact applied in the Rods From God concept of orbital bombardment. 

Retaliating

So you want to shoot back at the attackers. 

 U.S. Army’s Homing Overlay Experiment

Missiles can do the job. They are currently our only method of delivering weapons into orbital space. Something like an ICBM with an additional stage can reach LEO. Reaching higher orbits will require either a very large rocket, a high Isp engine for the upper stage or a launch system such a laser launch or ram accelerator.

However, each of these solutions have major issues when trying to shoot down an opponent in high orbit.

Laser satellite shooting down a missile slowly climbing to orbit.

Large rockets are easy to target and shoot down. A chemical-propellant rocket that needs to minimize its dry mass to achieve the necessary deltaV capacity will have very good acceleration but will end up being very fragile. Nuclear-thermal or nuclear-powered rockets can be much smaller and more durable, but getting sufficient acceleration out of them implies a very high power requirement, which might make them very expensive to throw at the enemy. 

Maglev track rocket launch system... vulnerable.

Regular launches take tens of minutes and cannot be disguised from the attackers. Shortening this window of vulnerability can be done by using a launch system that powers the rocket or accelerates it externally. However, the infrastructure for the launch systems will in turn become a priority target for the attackers. Massive, hard to hide and immobile, they will receive a lot of firepower. Some launch systems are practically impossible to shield from damage, such as a laser launch system that needs thousands of exposed laser optics, and others reveal their positions as soon as they fire a rocket. Building underground is also a very expensive endeavour when considering that all the work can be undone by a single 'bunker buster'-type weapon.

The logistics of launching missiles against attackers sitting in orbit works against the defenders. The attackers can de-orbit a missile by expending only a few tens to hundreds of meters per second of deltaV. A defender must equip each missile with tens of thousands of meters per second of deltaV. It might be easier to build more missiles and create rocket fuels on the ground at the start of the war, but after an orbital bombardment campaign by attackers with space superiority, it is unlikely to be the case.

Kinetics that can be shot all the way to high orbit need to handle hundreds to thousands of Gs of acceleration, traverse the lower atmosphere at dozens of kilometers per second, survive laser fire for several minutes with minimal capacity to dodge and take out a target with a very short window of interception. This is a tall order! 

Hot hydrogen light gas gun launch system. Can be weaponized.

So, what are the defender's options?

They need to retaliate with something that cannot be shot down, from a platform that can avoid counter-fire and can maintain functionality after infrastructure and services have been disabled world-wide. 

One option that fits the bill is laser submarines. 

Lasers cannot be shot down and hit their target instantly. They can be used so long as electrical power is supplied. Submarines operate underwater, an environment that can hide them until they surface and protects them from high-velocity projectiles and lasers while submerged. The can protect themselves this way for months on end, and if they employ the same life support systems as on spaceships, then it can add up to years. 

For the same reason that today's submarine fleets are considered an unbeatable means of retaliating against a foe after nuclear armageddon has wiped out the homeland, laser submarines will be able to operate and remain dangerous even after orbital attacks destroy all support infrastructure. 

Let us now look at how a submarine can be used to retaliate against attackers in orbit. 

The Challenges

Submarines are already equipped with a high electrical power generation. Large modern nuclear submarines are already able to produce over 100MW for years on end. In a futuristic setting with common space travel and space wars, power generation technology developed for interplanetary travel will allow submarines to produce gigawatts or more. 

Next generation water-cooled nuclear reactor.

The most likely generators for space travel will be nuclear due to their high power density. The biggest limitation to generating power from nuclear reactors is waste heat capacity: It is easy to heat up the reactor core but much harder to remove the heat. Submarines will have an entire ocean as a heatsink so will be able to produce more watts compared to a spacecraft with a reactor of the same mass and volume.

The Bi-modal NTR is a nuclear thermal rocket engine that doubles as power generator.

All of this electrical power can be used to power a laser generator. 

Three elements determine a laser's effectiveness: wavelength, radius of focusing optics and beam power. 

An observatory using a laser guide star.

We have already determined that laser submarines will likely be able to produce more electrical power than a similar laser space warship, so laser submarines will also have the advantage in beam power.

The radius of the focusing optics will depend on the specific arrangement of the laser weapon's components and how they are deployed. We will look into the possible designs down below. 

A free electron laser. Unlike most designs, it can freely switch wavelengths.

The wavelength however is not a variable laser designs have much control over. Submarines operate in an aquatic environment, on top of which is a hundred kilometers of Earth's atmosphere. At the interface of the ocean's surface is sea mist and suspended droplets of water in fog or clouds. The ocean's surface is not flat either, with waves of a few centimeters to a few hundred meters rolling over it endlessly. A beam emitted by a submarine will have to penetrate all of this environment and still travel the hundreds of thousands of kilometers' distance separating it from a target in high orbit. 

The optical properties of water are therefore the determinant factor for which wavelengths the laser should produce.

Here is the absorption spectrum of water:

The lower the 'Relative Absorption value', the less the wavelength's energy is absorbed. We can clearly see that the lowest values are for the 'optical window' that corresponds to the 400-700nm visual spectrum. The highest absorption is for 100nm ultraviolet wavelengths and 3000nm infrared wavelengths. 

Here is the absorption spectrum for our atmosphere:

The atmospheric attenuation of electromagnetic radiation has similar features to that of water: short wavelengths such as X-rays cannot go through while long wavelengths such as radio penetrate easily. 

It might be easier to consider the laser beam as being fired from space and coming down to the surface.

A 100nm ultraviolet laser beam will traverse the vacuum of space with ease, but will stop short of reaching the upper atmosphere. A 400nm blue laser will go through the atmosphere and through 460 meters of water before being reduced to less than 1% of its initial power. A 1000nm infrared laser will lose 20% of its power to the atmosphere and be completely absorbed by half a meter of water. A 100m radio wavelength just bounces off the ionosphere.

While shorter wavelengths are preferred for laser weapons, as they allow a beam to be focused to destructive intensities over longer distances, a laser submarine should use 400nm wavelength lasers to penetrate water and the atmosphere without losing a lot of beam power. 

The equation for how much of a beam's energy is retained after traversing a medium is given by:

• Percentage transmitted: e^( -1 * Attenuation coefficient * Depth) * 100

The attenuation coefficient is usually given in cm^-1, so the depth should be converted into cm units.

For example, near-infrared light at 800nm wavelength has an attenuation coefficient of 0.01cm^-1. We want to know what percent of a near-infrared laser's energy remains after passing through one meter of water.

One meter equals 100 cm. Per our equation, we find the percentage to be approximately e^(-0.01*100)*100: 36.8%. Just over a third of the beam gets through.

Here is a table of values for how much beam power is lost if the blue wavelength laser submarine fires its weapon at different depths, using an attenuation coefficient of 0.0001cm^-1:

We see that to maintain a good percentage of laser power getting through the water, a laser submarine would have to fire at rather low depths. According the the table above, a 10 meters depth using blue laser light looks like a good compromise: deep enough to escape orbital surveys and strikes, with at least 90% of the laser power going through.

So is a laser being fired at 10 meters depth a good idea?

Factors affecting a solid state laser weapon system.

The table gives an incomplete picture. While laser power being absorbed is an important factor to consider, there is a large number of other elements that affect how effective a laser is. One such element is thermal blooming. That 90% power transmission rate implies that 10% of the laser power is absorbed and goes into heating the water. If the laser power is rated in megawatts, the heat absorbed by the water becomes significant. Hot water has different optical properties compared to colder water - it will work as a lens in reverse, effectively de-focusing the laser. 

Another significant issue is the water/gas interface. When light travels between two mediums of significantly different density, like seawater and atmospheric gasses, it is bent by refraction. Even worse, the sea's surface is constantly disturbed by waves, tides and other movements. Instead of a smooth surface, which angling the laser can compensate for, it is continuously changing and bending light in different and hard to predict direction. Here is a familiar example of the effect: 

This effect is familiar to astronomers trying to gaze at stars through the moving atmosphere, and adaptive optics are used to compensate for the deviations in light traversing the atmosphere.

For a laser weapon, adaptive optics work in reverse. 

Adaptive optics cannot be employed as effectively when used underwater. While the atmosphere's movements are already difficult to detect and correct, trying to effectively measure how light moves through two mediums with a complex and moving interface is much harder. Guide lasers are used for measurement, with the light reflecting off the ionosphere creating an artificial 'guide star' for astronomers to calibrate their instruments. A guide laser placed underwater would submit to the same chaotic disturbances as the weapon laser and would be unusable. They would also have to work much harder. Refraction means that inaccuracies are multiplied once they pass through the water/air interface. 

Interference with sunlight works in both directions.

Finally, there's the problem of reflection. While water is decently able to let higher wavelength visible light penetrate, the massive difference in density between the water and the air (x1000) above it means that it is a good reflector. Laser light would travel from the submarine to the water/air interface, and just be bounced back below the surface. For sea water, less than 6% of the laser light would be reflected at angles below 30 degrees.

While the above table might not give any large figures, remember that the angle is measured against the rippling, swelling and rolling waves. A nominal angle of 10 degrees against the water's surface might transition between -20 and 100 degrees as a wave moves over a laser. This is the difference between 3% and 45% of the laser not going through the ocean's surface.

Submarines can survive this... but it might not be enough to matter.

The principal advantage of staying underwater is that the submarine will be protected from high velocity strikes and retaliatory laser fire. However, if it cannot return fire from this position, then it cannot serve as a perfect last line of defense.

The Solutions

So, based on the previous section, we can affirm that attempting to shoot a laser while underwater provides unequalled benefits but also significant challenges.

We can either tackle the problems a laser submarine faces directly or attempt to circumvent them.

-Long wavelengths

Previously, we considered that blue wavelengths were optimal for shooting while underwater as they were absorbed the least. The reduced absorption would have allowed a submarine to transmit over 90% of the laser power to the ocean's surface from a depth of 10 meters. However, the distortion at the water/air interface rendered this option impractical.

How about using a wavelength that is less efficient at penetrating water, but is less affected by distortion? 

Looking at the absorption spectrum of water, we notice that wavelengths longer than 100 micrometers are absorbed less and less as the wavelength increases. At 1m wavelength, the laser would traverse water as easily as blue light. This corresponds to a frequency of 300MHz. This is the radio band. 

Not coincidentally, frequencies of lower than 300MHz are used to communicate with submarines. At 3 to 30kHz, which is wavelengths of 10 to 100km, can penetrate the seas to a depth of several hundred meters. Using even lower frequencies further increases penetration depth, but would require impractically large lens to focus onto a target in high orbit. Another factor working against longer wavelength radio is that the ionosphere can reflect signals back down to the surface at frequencies below 30MHz.

A 1m wavelength radio laser will be able to traverse the atmosphere mostly undisturbed and go through the ionosphere without refraction. The features of waves are too small to cause it to wobble chaotically at the sea/air interface. The beam would bend coming out of the sea, but it is a single predictable deviation that can be corrected.

Inductive output tube diagram.

A radio-wavelength coherent beam or 'raser' can be generated by a Free Electron laser or inductive output tubes with an efficiency exceeding 70%.

The advantages of a radio-based anti-orbital system is that it allows a submarine to fire upon targets while deep underwater. Even at 20 meters depth, the radio beam would transmit 82% of its power through water and lose less than 1% going through the atmosphere. It is much less affected by small waves and other turbulence in the water, and mostly immune to above-surface weather effects.

There are several downsides however. Such a large wavelength makes it impossible to focus the beam down to destructive intensities without a very large radio dish - this might get impractical when you also want the submarine to move quickly while underwater. Another issue is that the beam won't interact with the target in a consistent manner. 

Lasers, for example, are absorbed by the outermost layers of the materials the target's surface is made of. The heating is concentrated in the 'skin' of the target. Sufficiently intense laser beams heat this skin layer to very high temperatures, causing the material to boil away or even explode. 
Radio beams would use wavelengths a million times longer that do not interact with the target's materials at an atomic level. They are much more sensitive to the conductivity of the materials they are striking. Good conductors such as steel or aluminium efficiently reflect radio waves and are not heated. Good insulators such as ceramics or glass are mostly transparent to radio waves and do no absorb the beam's energy as it passes through them. Radio absorbing materials have to be neither good conductors or insulators, such as 

This is bad news if the targets are space warships with an external metallic hull and an internal structure based on advanced carbon-composite and ceramic materials. Large propellant tanks will let the radio waves pass straight through. Small features of 10cm or smaller are completely invisible to the radio waves too. 

However, there will still be ways to deal damage. 

Openings in the metallic hull would allow radio waves to enter and then bounce around on the internal surface. Like a microwave oven, the trapped radiation will pass through radio transparent materials thousands to millions of times before being fully absorbed. A human is mostly composed of salted water. He or she would absorb about between 0.1 and 1% of a radio beam going through their body. If the radio beam stays inside a 10m diameter hull for just 76 microseconds, 2300 bounces are possible and the percentage of beam energy absorbed rises to 90%. When the beam power is measured in tens to hundreds of megawatts, this has dire consequences for a human crew. 

Another effect is induced current. If even a few watts manage to circulate in microcircuitry, it is enough to short-circuit or even melt down computers, avionics and delicate sensors. RF Shock and Burn is a serious issue for electricians and engineers working on conductive structures near a high frequency radio source. At the power levels radio-laser submarines will pump into targets, induced current is enough to melt steel.

Steel melted by 1-30kHz radio frequencies.

Modern submarines are not powerful enough to compensate for the diffraction of a 1m wavelength radio beam. With 100MW of available electrical power, 30% of which is lost in an inductive output tube and another 10% to seawater and atmospheric absorption, less than 63MW will reach space. Even the largest submarines, such as the Ohio-class SSBN, have a hull diameter (beam) of 13m. Mounting an internal dish to focus a radio beam up to this diameter will create a very low performance laser. 
Targets at 10km distance will receive about 22W/m^2 - a great radio signal, but a terrible weapon. Targets in low orbit and high orbit will receive milliwatts of power. 

A 1296MHz dish. For 300MHz beams, the spaces can be even larger.

What is needed is much more power and an externally mounted radio dish. Thankfully, a 300MHz beam can be focused by a dish with holes up to a tenth of the wavelength in size. A radio dish for this wavelength can is very lightweight and easily collapsible, with conductive spars spaced by 10cm lengths. The spars can be made hollow to have neutral bouyancy, allowing them to support themselves without many structural elements. At 10m depth and below, there are few disturbances in the surrounding water.

Dish diameters of 100 meters or more are envisageable, massing less than 1kg per m^2. Tension wires hold the shape and serve as the mechanisms for adaptive optics to act on the dish. 

A group of submarines using space-grade nuclear reactors might be able to put together 500GW of power with a combined reactor mass of only 2500 tons. Between them, they can hold up a dish 1km in diameter, as follows:

This arrangement allows the submarines to focus a 315GW beam to an intensity of 67kW/m^2 at an altitude of 1000km. For low orbit targets, the intensity is 1.67MW/m^2. These intensities are far from enough to melt or physically damage the structure of a spaceship. However, the beam is large and entirely envelops the target. Any hole through a metallic exterior or any cavity lined by a radar reflector will turn the spaceship into a microwave oven receiving megawatts of heating over time. At high altitudes, the intensity is lower by the targets orbit much slower, giving the Rasar beam time to boil crews to death and melt components directly or indirectly. 

-Interface lens

A variant on the lens used for above.under water filming.

The biggest trouble with optical wavelengths is the chaotic distortions and reflections created by the sea/air interface. They would allow submarines to physically damage targets with relatively small lens and shoot on the move, but aiming though the interface seems impossible...

... unless an interface lens is used.

It is an optical array that floats on the ocean's surface, serving to handle the beam's transition from underwater to atmospheric mediums. Glass can be made to have a refractive index similar to that of water. A laser beam traversing a sea/glass interface would not suffer any distortion. This is the reason why some transparent objects disappear completely while underwater - our eyes cannot make out any distortions that reveal their presence.

The refractive index of the polymer ball is exactly the same as water.

The interface lens can also serve to focus the laser. It can be made much larger than whatever the submarine can carry, as it is not confined by hull dimensions or hydrodynamics. 

One primary advantage of these floating structures is that they can be deployed before firing commences, and each is much cheaper than a submarine. When a target passes overhead in orbit, a laser submarine can rise to firing depth and start shooting. It only needs to equipment to focus the beam from the laser generator to the interface lens, a distance of ten meters or so. The floating lens receives the beam, corrects the angle and aims at the target overhead. If the target is not destroyed, it can trace the laser back to its origin and initiate a retaliatory strike. 

An interface lens is not very mobile and needs to stay on the surface, so it cannot protect itself by diving. There is a good chance it will be destroyed... at which point the laser submarine switches to firing through another interface lens and so on. 

Although the lens will have to be rather large and heavy to receive a laser beam from a wide variety of angles underwater, and re-focus it in a moving target hundreds of kilometers above, which makes it expensive, it must be considered as an expendable asset when compared to cost and size of a nuclear submarine. Also, the lens can be covered by an isothermal sheet and made out of materials transparent to radar, making it hard to detect from orbit until it starts firing.

Using a 10m diameter interface lens, even a modern submarine with 100MW of available output will be able to deal serious damage to targets in low orbit. About 40MW of the submarine's power will reach the target using a diode laser generator at 400nm wavelength, but at an intensity of 133GW/m^2 at 200km altitude. This is enough to rip through 14.8 meters (!) of aluminium per second, or even 6.5m/s of carbon armor. Any target caught by this beam for even a second will be cut in half. At 1000km, its performance is still a respectable 52mm/s through carbon.

Spaceship in Children of a Dead Earth scarred by laser strikes.

More advanced submarines can get away with smaller lens that are harder to counter-attack and still deal devastating damage to high orbit targets. A 10GW laser beam focused through a 4m wide interface lens can blast away targets at a rate of 837mm/s at 1000km. 

Disadvantages of this system is the cost of 'expendable' large adaptive mirrors and possibly the inability to use floating structures in severe storms with large waves rocking the optics. 

-Towed Lens

This fixes the problem with floating optical arrays. The laser is focused by towed apparatus that can be held underwater until firing starts, and then moved around after an initial volley to avoid counter-fire. 

The towed lens can be lighter and cheaper than a fully independent floating lens. Electrical power, computing operations and other functions can be provided by the submarine towing the lens, with only the actuators and suspension retained.

Lasers have been carried through optical fibres with nearly zero losses of beam energy over distance. This is because internal reflection of the beam is done at grazing angles within the optic fibre. In other words, laser beams of megawatts to gigawatts power levels can be transported by optic fibres without any significant losses and no special provisions against heating. 

Optical fibres can carry a laser generated by a submarine to the towed lens, and they can run parallel to the load bearing cables attaching the lens to the submarine. This method of delivering the beam to the lens bypasses the losses and complications of having the beam penetrate several meters of water to reach the surface. 

To these advantages come some downsides. The submarine becomes more vulnerable that if it relies upon fully independent floating lens. If an enemy target locates a floating lens, it might correctly assume that the much more valuable submarine is very close to the lens. When a target spaceship in orbit sends down counter-fire before the submarine is ready, the latter would be forced to cut loose the lens and dive... this breaks the optical fibre cable and renders the lens useless. 

Tactics using towed lens might involve dragging along a fleet of lenses and rotating them to the surface and back. Longer fibre optic cables gives the submarine more freedom to move, while a mix of decoys and intermittent and random firing patterns reduces the disadvantages of the design. 

-Optical phased array floater.

Do away with the submarine!

A specialized vehicle can be built solely for the purpose of hiding a laser weapon underwater and surfacing for short bursts of fire. Since this weapon only attacks from above the water and does not have to worry about hydrodynamics, nifty solutions such as an optical phased array can be used. The laser generator's size is equal to the lens diameter and if it received damage, it will only suffer reduced output. 

Instead of VLS cells, phased array grids?

The more delicate components such as the power generator can remain submerged, only transporting electricity to the phased array on the surface through cables. A reactor embedded in the sea floor can be a very difficult target to locate and destroy.

-Supercavitating platform. 

'Bullet submarines' powered by excessively powerful nuclear reactors.

If submarines have access to gigawatts of power, they can also use it for propulsion.

This level of power output can enable submarines to reach supersonic speeds through supercavitation through water. If they can rise to the surface, fire, dive and relocate in a matter of seconds, then they can evade counter-fire through sheer agility. 

It might be best in this case to mount a set of optical phased array lasers tailored to trans-atmospheric wavelengths to be used once a submarine surfaces. Gigawatts of power means gigawatts of heating: the local atmosphere can be cleared of moisture and mist that distorts the beam most heavily. 

A 1GW laser at 400nm focused by even a relatively small 4m diameter lens can blast past 23.7m/s of aluminium or 10.4m/s of carbon at 200km, and remains deadly at 1000km with 83mm/s of carbon penetration. This allows for short bursts of laser fire to take down any target.

Atmospheric lensing.

Advanced techniques such as thermal lensing using the Kerr effect is being developed in programs such as the Laser Developed Atmospheric Lens (LDALs) by DARPA. LDALs can allow high-power submarines to extend their effective range to tens of thousands of kilometers while reducing the effectiveness of laser counter-fire. 

Conclusion. 

Lasers and underwater environments don't mix well, but there are many solutions to gain the protection a submarine enjoys while attacking instantly and repeatedly with direct energy weapons. 

Once these solutions are applied, a defending planet with deep oceans can hope to maintain an effective last line of defense against invading spaceships.