Energy Storage

Science fiction is full of flashy technology. Incandescent beams. Hover sleds. Menacing robots. Spaceships with obscure engines pumping rocket plasma into the void of space. Unexplained glowing things cluttering up engineering bays and mad scientist's workshops. But all these things need energy. And if you are not making use of the energy as soon as it is generated, you need to store it. Here, we'll discuss some of the ways that energy can be stored in order to power all of these wacky tech ideas.

Material limits

Most things that store energy rely on the chemical bonds between atoms to either actively shuffle the electrons around, provide heat through chemical reactions that is fed into a heat engine, or to simply hold the energized structure together. The first two of these are generally well appreciated – a battery or fuel is no better than the ability of its chemical reactions to supply energy. The stresses imposed on the materials by the energy circulating inside the device is often less considered, but poses the ultimate limit for many of the devices described here. Consequently, to get the highest specific energy you want to use the highest possible specific strength (strength-to-weight ratio) material for making the disk. The best performing steels (maraging steels) can get you around 0.2 to 0.3 MJ/kg. Carbon fiber can reach 2.5 to 4 MJ/kg, depending on type, with some recent samples promising 6 MJ/kg. The ultimate limit for materials held together by chemical bonds is the carbon-carbon bond found in things like atomically perfect graphene or carbon nanotubes. In principle, these could reach 45 to 60 MJ/kg if they could be made defect free (or in configurations that are resistant to crack propagation because there will inevitably be defects) and in bulk samples.

Motors and generators

An electric motor takes electrical energy and transforms it into mechanical energy. When run in reverse it becomes a generator, taking mechanical energy and turning it into electrical energy. Note that these are the same machine – any electric motor can be run backwards as a generator and vice versa. With modern (2021) tech, electric motors generally have an efficiency of 90 to 95%, with 99% efficiencies reported for experimental superconducting designs. Most modern electric motors have specific energies in the 1 to 2 kW/kg range, with a few that have been engineered to hell and back for ultra-high performance bleeding edge mass reduction to just barely break past 10 kW/kg.

Electrical energy storage

Supercapacitors

Also called ultracapacitors, supercapacitors store energy in the separation of charge that occurs at interfaces via various complicated mechanisms like redox reactions, formation of electric double layers, or intercalcation. They can discharge much faster than batteries, so if you are limited by power rather than energy you might choose supercapacitors over batteries - you'll be able to shoot more rapidly, but with fewer shots. Supercapacitors can also survive many more recharging cycles than modern batteries, but lose their charge faster (losing most of their charge in a few weeks). The very best modern (2021) commercial supercapacitors store somewhere around 50 kJ/kg and discharge at a rate of about 15 kW/kg. So for high power pulsed applications (like many directed energy weapons) you will still want to accumulate that electrical energy in a solenoid or dielectric capacitor for a higher power but brief discharge that lets you reach the peak power needs of your device. However, laboratories around the world keep hinting at even higher capacity supercapacitors that can store even more energy, so who knows what the future will bring.

Batteries

Batteries store energy in chemical reactions or aqueous ion migrations that drive currents of electrons. Batteries store more energy than supercapacitors, but release it more slowly. To get a reasonable rate of fire, you will need large battery packs to meet the average power requirements – but that large battery pack will give you a very large number of shots. Like supercapacitors, a battery for a pulsed laser will almost certainly be energizing a faster discharging electrical circuit element like a dielectric capacitor or an inductor. Alternately, you might use a battery to charge a supercapacitor. This could get you several shots at rapid fire at a time from the supercapacitor, with an overall high number of shots from the battery but with a waiting time to charge up the supercapacitor after you empty it. As usual, the supercapacitor would need to discharge into a more rapidly discharging circuit element for pulsed applications.

Lithium-ion battery

The modern standard is the lithium-ion (Li-ion) battery. These batteries store lithium ions packed between the atomically thin layers of a graphite anode. When the battery discharges, the ions migrate through an electrolyte to be absorbed into a metal oxide cathode layer (usually cobalt oxide, for the high energy storage, but iron phosphate or manganese oxide are also used). As of 2021, commercially available Li-ion batteries can store somewhere between a third and one MJ/kg (so 6 to 20 times more than the best modern supercapacitors), and discharge at a rate of about a quarter to a third of a kW/kg (or roughly 100 times less than a supercapacitor). They have a self-discharge rate of about 2% per month, a charge-discharge efficieny of 80 to 90%, and last for something like 1000 charge-discharge cycles.

Lithium metal batteries

Lithium metal batteries are a potential near future battery technology. They replace the graphite anode of the Li-ion battery that simply collects ions between the graphite sheets with a layer of lithium metal. In combination with a solid state electrolyte, they might get specific energies of about 2 MJ/kg, or twice as much as a Li-ion battery. We can make lithium metal batteries today, but they can only handle a few dozen charge-discharge cycles before shorting out (and potentially catching fire!). There's a lot of research trying to find ways to make them last longer and be safer. By the time we're ready to equip our troops with laser rifles, we might have ironed out these difficulties.

Lithium sulfur batteries

Lithium sulfur batteries replace the cobalt cathode of a Li-ion battery with sulfur. Sulfur weighs less than cobalt, so you can cut down on the weight even more. How much more? We don't know yet. Most of the research these days involve ways of keeping the batteries from getting clogged up with unwanted lithium-sulfur compounds, greatly limiting their life. Maybe some sort of lithium metal sulfur battery with a solid electrolyte could reach 2.5 or even 3 MJ/kg? We'll eventually figure it out, but in the meantime we'll need to be patient and wait for the researchers to do their stuff (or, you know, because we are making science fiction, make something up).

Lithium-air batteries

Lithium-air batteries might be the ultimate in battery technology. You would have lithium metal at the anode and lithium oxide at the cathode, with a current of lithium ions being passed between them through the electrolyte and a current of electrons giving you your electric power to balance the charges. Up to 6 MJ/kg has been demonstrated in the lab (as of 2021); but the theoretical maximum specific energy is 40 MJ/kg! This, of course, is excluding the weight of the oxygen, which is assumed to be freely available from the air. But for all their promises, there are many challenges. Both their charging cycle lifetime and charge-discharge efficiency are disappointingly low, meaning that they will probably remain in the laboratory rather than store shelves for some time to come.

Superconductive magnetic energy storage

Inductors, like capacitors, are electrical components that can directly store electrical energy and discharge it quickly. An inductor is made by flowing electrical current and the reluctance of the magnetic field that current creates to change its strength. When you try to change a magnetic field, you get the production of an electric field that acts to drive currents in the direction that would maintain the field. This "magnetic inertia" is called inductance. If you have a device with a large inductance, interrupting the flow of current will start to decrease the stored magnetic field resulting in a "backlash" as the field resists the changes and creates a large voltage to ram more current through to maintain itself. In this way, you can consider the magnetic field itself to be storing the energy and it is often most convenient to consider it in this way when doing the physics.

Usually, inductors are made in the form of solenoids - a coil of wire wound in a tube shape. The problem, of course, is that in normal materials electrical resistance will almost immediately drain away all your energy in the form of heat. You might be able to use large inductors to build up energy over a fraction of a second from a more slowly discharging power source and then suddenly switch it all at once to ram that electricity through your laser at very high power. But for any long term energy storage with inductors you will need to use those exotic materials called superconductors.

Superconductors allow the flow of electricity through them without any resistance at all. In this way, a superconductive solenoid can be used for Superconductive Magnetic Energy Storage (SMES). To limit the exposure of the environment to the extreme magnetic fields created, the solenoid tube is usually bent around so the ends connect, making a shape like a bagel or doughnut called a torus. Once charged up, the supercurrent flows endlessly around surface of the torus creating a very high magnetic field that is confined entirely to the inside of the torus tube. Without this bending, anyone near one of these SMES would be in danger of being punctured by flying ferromagnetic metal objects or suffering from inductive currents zapping their body if they moved past too fast.

There are several limits on SMES's ability to store energy. The first is that all known superconductors can only remain superconductive at cryogenic temperatures, generally requiring liquid nitrogen to work. Room temperature and pressure superconductors may be possible, but we haven't discovered any yet and it is also possible that none may exist at all. If a superconductor's temperature exceeds this critical temperature, it quenches, or becomes non-superconductive. The sudden resistive heating from all the SMES energy being driven through the quenched superconductor can cause arcing, vaporization, and explosions.

Second, superconductors only remain superconducting up to a critical magnetic field. This critical field depends on the temperature (and goes to zero at the critical temperature). If the field exceeds the critical field, again the superconductor will quench. This means you will want to keep the operating temperature of the SMES well below the critical temperature at which it becomes non-superconducting. The energy density of the SMES depends on the magnetic field it contains:

$E/V=0.4\times B^{2}\,{\mbox{kJ}}/{\mbox{liter}}$

where $B$ is the magnetic field strength in tesla, $E$ is the stored energy, and $V$ is the interior volume of the torus tube.

Third, while electric currents create magnetic fields, magnetic fields in turn exert forces on electric currents. Including the electric currents that are generating them. These self forces act to push the SMES torus apart. If the structure of the SMES is not able to handle the tensile forces, it will break and explode. This is what sets the upper limit on the specific energy – the strength of the backing material wrapped around the torus tube to keep the solenoid together. The specific energy of the SMES is thus limited by the material limits of their backing.

In principle, you can discharge a SMES essentially instantly. Flip a switch to re-route the current going through it into an electrical load and all of its energy can be dumped at once. In practice, any electrical system will have some capacitance which gives a finite time to the discharge – the inductor will ram its current into the load, but the capacitance of the load will store some of that energy as charge separation that builds up to resist the inductor's push. The capacitor connected to the inductor forms an electrical device called an LC circuit (or LRC circuit, when resistance is added as well), where energy will be sloshed back and forth between the capacitor and the inductor (and bled off by the resistance). One cycle of oscillation takes a time of $2\,\pi \,{\sqrt {L\,C}}$, where $L$ is the inductance of the SMES and $C$ is the capacitance of the load. So to fully discharge the SMES, it will take half of a cycle, or $\Delta t=\pi \,{\sqrt {L\,C}}$. When you add in the resistance of the load, things get a bit more complicated and you're likely going to end up with an overdamped response, but this very basic analysis still shows several things: you can have very high specific powers from a SMES, and to maximize the specific power you will want to minimize the inductance of the SMES and the capacitance of the load. Unfortunately, the amount of energy you can store is proportional to the inductance. One way to get the best of both worlds is to tap the SMES from multiple switches along its length, effectively separating the system into a number of separate inductors discharging in parallel.

An additional issue when working with large inductors is the switching problem. As soon as you start to throw a switch to divert the current from the inductor into the load, you get a small gap just as the switch is breaking the electrical connection that is interrupting the flow of current. The inductor's response is to concentrate all of the voltage it generates across this tiny gap in order to maintain its current. This generates an electrical arc, producing a low resistance path shorting the switch. As the switch continues to move apart, the arc grows so that it continues to connect the two terminals of the switch. This short circuits the whole circuit path, preventing any electricity from getting to the load. It also drops a lot of energy suddenly into the switch, likely frying the switch, ruining your SMES, and quite possibly causing an explosion. There are ways around this. For example the load might be connected to terminals shorted by a section of superconductive wire. If the wire is uniformly quenched, you end up with a sudden high resistance path across the wire and a lower resistance path through the load, and so the current is shunted through the load instead of causing an unwanted arc.

Mechanical energy storage

Flywheels

Flywheels use the inertia of a spinning disk to drive a mechanical load. To recharge, a motor is used to spin the disk back up. The limit to how much energy it can store is when the centrifugal force at the rim exceeds the strength of the flywheel material and the flywheel tears itself apart. The specific energy of the flywheel is thus limited by the material limits of the disk. But that's just for the spinning disk. For applications requiring electricity, you also need your electric motor/generator. For pure mechanical applications, you will need a clutch and driveshaft and gearbox and transmission. On top of that, you will need a housing (to reduce losses due to air friction by keeping it in vacuum, and to protect the outside world in the event of a failure) and low-friction bearings to allow the flywheel to keep spinning as long as possible. Self-discharge is quite high. With magnetically levitated bearings, self discharge rates are typically about 1% per hour (compared to 10 to 50% per hour for mechanical bearings). Superconductive bearings (which with today's materials must be cryogenically cooled - another source of loss with the addition of a cryogenic liquid logistics train) can reduce this to about 0.1% per hour (or something like 2% per day). But this all assumes that the bearings are only supporting the weight of the flywheel, not any gyroscopic precession torques. Any motion that tends to move the spin axis will lead to gyroscopic effects that will make the flywheel (and thus the laser weapon) very hard to point and maneuver and also greatly increase the self-discharge rate. Mounting the flywheels in counter-spinning pairs will solve the first of these two problems, but not the second. If you are designing for any kind of mobile laser weapon, you will need to put the flywheel energy storage system in gimbals to allow the spin axis to remain constant. Even for stationary applications, you need to be sure the flywheel spin axis is aligned with the planetary spin axis to avoid daily precession cycles. On the plus side, flywheels allow for nearly unlimited charge-discharge cycles without any degradation.

Springs

Hypothetically, something like a watch spring could be used to drive a mechanical device or run an electric generator. To recharge, a motor would wind the spring back up again. This has the usual material limits on specific energy, and the specific power limits from the electric motor or mechanical drivetrain. You have the benefit of nearly no self-discharge, and no need to worry about gyroscopic forces. However, this is a largely untested technology and its limitations are not well understood yet.

Credit

Author: Luke Campbell