MICROWAVE THERMAL ROCKETS

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WHY DO WE NEED THEM?

The U.S. government is spending $44Bn on launch-related activities from FY2014 to FY2018 (GAO-13-802R).  This equates to $212M per week.  Of this, 25% is being spent on R&D, and 75% on building rockets, launching them, and related non-R&D activities.  Despite this economically significant expenditure, the U.S. government launches payloads into orbit the same way it did in 1965; by chemical rockets.

Traditional expendable rockets achieve payload fractions of less than 4.2%.  The rocket equation shows how this insufficient payload fraction results from the specific impulse (Isp) of chemical propellants, which long ago reached a practical limit of 460 seconds by reacting hydrogen with oxygen.  The LOX/LH2 reaction releases 16 MJ per kilogram of propellant mixture, whereas the specific energy of low earth orbit (LEO) is 32 MJ/kg.  Conventional rockets reach orbit only because the propellants they expel make them lighter as they go.  Additionally, rockets are structured into multiple stages so that structural mass is periodically jettisoned as well.  Even then, small fractional increases in the structural mass can displace the entire payload mass.

The price of payload delivery to low earth orbit (LEO) as a function of rocket payload capacity. 

The price of launch remains above $10,000 per kilogram of payload delivered to low earth orbit for most models of rocket, as shown in the interactive chart above (click ‘1’ or ‘0’ to show or hide layers).  The data points are rockets from many countries spanning 60 years and representing hundreds of billions of dollars in evolutionary R&D investment.  In contrast, the energy cost of launch is below $100 per kilogram.  The two order of magnitude difference between these two costs arises because, ultimately, traditional chemical rockets are a marginal technology for the purpose of launch to orbit.

Propulsion figures of merit

Forms of propulsion organized by the main metrics of T/W ratio and Isp.  Data points are actual engines, grouped by type.

Directed energy rockets bypass key limitations of conventional rockets, and in so doing are easily able to reach orbit using a single stage, as opposed to the 2-4 stages used for conventional rockets.  A microwave or laser thermal propulsion system combines the specific impulse of a nuclear thermal rocket engine with the thrust to weight ratio of a conventional rocket engine, and the result on system performance is profound:  For a given rocket, the payload mass is increased by a factor of 3 to 12 times.  In addition to this direct effect, which can be shown using the rocket equation, there are additional cost savings that arise from using 1 propellant instead of 2, and 1 stage instead of 2-4 stages.  The combined effect of these savings is large, so that the overall cost is a factor of 6 to 144 times lower than a conventional rocket, depending on the particular assumptions made.

ORIGINS OF THE 4 MAIN TYPES OF DIRECTED ENERGY PROPULSION

Konstantin Tsiolkovsky is well known as one of the fathers of rocketry and astronautics.  He was the first to derive the rocket equation in 1897.  Less known is that Tsiolkovsky himself proposed directed energy rocket launch via a “parallel beam of shortwave electromagnetic rays” in 1924 (Tsiolkovsky 1924).  The two-pole magnetron had been invented only 3 years earlier, and the time average power output at that time was so low that it would take the coherently combined output of millions of such devices to power a microsatellite-class rocket to orbit.  In his 1924 book, Tsiolkovsky estimates that, due to diffraction, a ground-based beam director requires an aperture diameter of 12.6 km to produce a beam concentrated enough.  He wonders how any receiving material can withstand the intense heat generated by the beam, and how it can be directed onto a rocket as it ascends to orbit, eventually concluding that “This method of imparting velocity raises quite a few difficult problems, the solution of which I shall leave to the future.”

In 1959, Willinski proposed for the first time a vehicle wherein “beamed power would be utilized to heat a propulsion fluid, such as hydrogen, ammonia, gasoline, or even water, which would then be expanded through a nozzle to produce thrust” (Willinski 1959).  Noting the problems of large apertures and beam diffraction at longer wavelengths, and the opposing problem of atmospheric absorption at wavelengths shorter than 10 cm, Willinski dwelled predominantly upon a receiving antenna in the form of a large inflated balloon capable of focusing microwaves onto a central heat exchanger.  Due to drag, the vehicle is constrained to operate as an upper stage above the atmosphere.  Significantly, Willinski mentions that “the skin of the vehicle itself could possibly be utilized as a surface antenna, thereby allowing operation in the atmosphere.”  This line of reasoning is consistent with the later microwave lightcraft (Myrabo 1995).

In 1972, the idea of using a pulsed laser to propel rockets to orbit was proposed separately by Kantrowitz and Minovitch (Kantrowitz 1972, Minovich 1972).  The laser had been invented only 12 years earlier, yet it took another 20 years before laser thermal rockets, shown on the bottom left of the figure below, were proposed by Jordin Kare (Kare 1992).

The 4 main approaches to directed energy propulsion

The four main approaches to directed energy propulsion form a grid.  The bottom right approach was proposed in 1972 (Kantrowitz 1972, Minovich 1972), the bottom left in 1992 (Kare 1992), the top left in 2002 (Parkin, Culick et al. 2002), and the top right in 2003 (Oda, Nakagawa et al. 2003).

Throughout this time, microwave sources grew in power and frequency.  While long wavelength microwaves sources led Tsiolkovsky and others to estimate aperture sizes exceeding a kilometer, shorter wavelength sources enable aperture sizes on the order of 100 meters and increase the beam intensity at which plasmadynamic breakdown occurs by several orders of magnitude, allowing denser vehicles that are more like conventional rockets.  At this time, microwaves have the major advantage of being 1-4 orders of magnitude cheaper than lasers on a $/Watt basis (0.1-10 $/Watt vs. 100-1,000 $/Watt), and they are unaffected by atmospheric scintillation and more tolerant to weather, particularly at the lower frequencies below 35 GHz.

The lower cost of microwaves motivated Kevin Parkin to invent a microwave-powered launch concept in 2002.  He named it the microwave thermal rocket because it used a heat exchanger in place of a combustion chamber, as does the nuclear thermal rocket.  By dispensing with combustion, the rocket performance is improved so much that it becomes capable of ascending all the way from the ground to orbit using a single stage and increasing its payload as it does so (Parkin and Culick 2003, Parkin, DiDomenico et al. 2003).

TERMINOLOGY: MICROWAVE VS. MILLIMETER-WAVE

The common usage of the terms ‘microwave’ and ‘millimeter-wave’ depends on context.

In the overall context of the electromagnetic spectrum, the word ‘microwave’ is conventionally used for an electromagnetic wave at a frequency between 1 GHz and 300 GHz.

In the context of microwaves, the term ‘millimeter-wave’ is conventionally used for an electromagnetic wave at a frequency between 30 GHz and 300 GHz.

In the context of this website, we use ‘millimeter-wave thermal rocket’ to denote a rocket that operates at a frequency of 30 GHz to 300 GHz.  We use ‘microwave thermal rocket’ to denote a rocket that operates at a frequency of 1 GHz to 300 GHz, though we try to use the more specific term of millimeter-wave thermal rocket where applicable.

HOW IT WORKS

The current concept benefits from 13 years of feedback and design evolution.  A single foil balloon tank holds a slush methane propellant.  This propellant is then pumped through the heat exchanger, reaching close to the temperature of an incandescent light bulb filament just prior to being expanded through a spike nozzle to produce thrust.  The beam tracks the heat exchanger, which faces the general direction of the beam throughout the ascent to orbit.  There is only a single propellant, single tank, single turbopump, and single stage all the way from the ground to orbit.

Concept of how a microwave thermal rocket will operate

The concept of operations for a microwave rocket is shown above.  In the simplest implementation, launch begins from the ground and begins vertically upwards.  After a short time, a long-range beam director acquires the rocket.  The rocket turns and accelerates horizontally until it reaches orbit, and then the payload is released.

Distribution Statement A – Approved for Public Release, Distribution Unlimited.
A beam heats prototype heat exchanger tubes to > 2,000 K for the first time in tests conducted on the 13 August 2013 at the General Atomics DIII-D Fusion Reactor in San Diego as part of the DARPA-NASA Millimeter-wave Thermal Launch System Program.

The video above was a key milestone during a test campaign using a 110 GHz beam at the General Atomics DIII-D Fusion Reactor in San Diego California. This was the first time that Mullite heat exchanger tubes were heated to very nearly their melting point by the beam, thanks to an idea to coat them internally with a thin layer of graphite to act as an absorber.  These tubes were used as the basis for a heat exchanger that was mounted to a small rocket and launched to just a few tens of meters altitude in early 2014.  With refinement, their performance should be sufficient for the orbital rocket.

WHAT IS THE ECONOMIC/BUSINESS CASE?

The feasibility and performance of the microwave thermal rocket is supported by many analyses over the past 13 years sponsored by Caltech, NASA, DARPA and the U.S. Air Force.  Over this time, various methods have estimated that the microwave thermal rocket can reduce launch costs by 1-2 orders of magnitude.  We periodically add new estimates, but there is little new to be gained and each week of delay in implementing microwave thermal rockets ultimately costs about $200M.  Consequently, our focus has shifted to minimizing the infrastructure cost of an initial system.  This focus on infrastructure cost begs the question; over a given payback period, how low must the initial infrastructure cost be for a directed energy launch to make economic/business sense?

Initial infrastructure cost is currently driven by the beam director cost, which itself is comprised of the cost of the microwave sources plus the cost of reflecting aperture.  Initial infrastructure cost can be expressed in $/Watt and is its most important figure of merit.  The $/Watt value at which microwave launch becomes economically superior to present launch systems is calculated below under various assumptions and over a payback time of 20 years.

Cost benefit analysis

In the baseline case above, there continues to be no microwave thermal launch system, and 100% of the market is served by families of conventional chemical rockets, the largest of which is capable of launching a 20 metric ton satellite to LEO.  The cost of launch to continues to be $159M/week for the U.S. Government, excluding R&D.  This equates to a $165Bn expenditure over the 20 year period.

In the pessimistic case, a microwave rocket with a 200 kg payload capacity to LEO captures 1% of the total revenue for satellite launch.  It has a relatively poor jet power per unit payload mass (though not the worst), and a relatively poor cost reduction factor.  Consequently, its initial infrastructure needs to cost less than $2/Watt in order to save money over the period.  Current estimates of beam director cost are 1-5 $/Watt at this scale, and further research is expected to lower this value and its associated uncertainty.

In the optimistic case, a family of microwave rockets capable of launching up to 20 tons to LEO captures 100% of the revenue for satellite launch, replacing traditional rockets altogether.  They have a relatively good jet power per unit payload mass (though not the best) and a relatively good cost reduction factor.  Consequently, the initial infrastructure needs to cost less than $27/Watt in order to save money over the period.  Current estimates of beam director cost are 1-2 orders of magnitude below this value, depending in part on the choice of frequency.

The interpretation of these results is that a business case does not yet exist for a 200 kg microwave thermal launch system that fits within the cost, risk and schedule of private capital.  More work is needed to lower technical risks, and in particular to define the beam director and constrain its associated costs. That being said, the economic case to replace traditional rockets with microwave thermal rockets is compelling, and there is every reason for the U.S. Government to make substantial R&D investments toward the initial goal of a small microwave thermal launch system.  This would be a technology push without regard to the cost impact on launching small satellites, since the overwhelming economic compulsion originates from the rest of the market.

THE BOTTOM LINE

The conventional rocket industry reached maturity many decades ago and the U.S. Government spends $212M per week on it. Hundreds of billions of dollars have been spent on researching and developing families of rockets and launching them. Directed energy launch was proposed almost 100 years ago by Tsiolkovsky himself, and one by one, the conditions needed for it to become economically superior have fallen into place: Lasers were invented. Vacuum and solid-state microwave sources were invented. The $/Watt for beam sources fell by orders of magnitude. Detailed concepts were invented for pulsed laser rockets (1972), laser thermal rockets (1992), microwave thermal rockets (2002), and pulsed millimeter-wave rockets (2003). Of these, the laser and microwave thermal rocket engines outperform chemical engines in T/W and Isp. And of these, microwave thermal rockets have the lowest initial infrastructure cost as measured in $/Watt. Assuming that the U.S. Government is the only customer, simple cost-benefit analysis shows that the $/Watt is already low enough to compel a changeover from chemical to microwave thermal rockets.

FREQUENTLY ASKED QUESTIONS

WHAT IS THE MAXIMUM PAYLOAD?

There is no maximum payload mass for the microwave thermal rocket.  The launch system, which includes the beam director, can be scaled up to launch all payload classes, through 1 metric ton payloads and even above 100 ton payloads, if needed.  Once a system is built that can launch small satellites, there is every reason to scale it up.

WHAT IS THE MAXIMUM BEAM DIRECTOR SIZE/POWER?

Due the physics of beam diffraction, beam directors become smaller as the rocket size (and payload capacity) increases.  For these, the limiting factor is power density, or, depending on the way in which microwave sources are combined to form a single beam, it can be spectral characteristics that limit the number of microwave sources per beam director.  However, these limits are for a single beam director.  Once one beam director has been built, there is no reason a second cannot be built and reuse the same spectrum.  Both can then be trained on a single rocket designed for double the power, and due to efficiencies of scale, the rocket payload mass will more than double.  Any number of beam directors can be trained on a single rocket in the same way that overlapping spots from flashlights do.

WHAT IS THE MINIMUM BEAM DIRECTOR SIZE/POWER?

Due to the physics of beam diffraction, beam directors become larger as the rocket size (and payload capacity) decreases.  Above a certain aperture size, it minimizes the overall cost to build more microwave sources and spill more energy than to further increase the beam director size.  Curves for cost-minimized beam directors have been plotted and it turns out that lighter rockets always result in a cheaper beam director.

HOW MUCH POWER DOES IT TAKE?

10 MW of ‘wall plug’ power per kg of payload for the lightest rockets, falling to below 1 MW/kg for the heaviest rockets.  This is because the payload fraction and transmission efficiency both improve as the rockets become heavier.

HOW MUCH OF THE PAYLOAD COST IS FOR POWER?

$30-100 per kilogram of payload.

HOW IS THAT MUCH POWER GENERATED?

The power needed by the thermal rocket engines is comparable with the power developed in conventional rocket engines of the same thrust, though of course this power is generated on the ground for thermal rockets.  Up to 2 GW can be obtained directly from the electrical grid for beam directors that are located near to high capacity transmission lines, for example in California, and this is enough to launch a rocket with a payload of about 100 kg.  This power would cost on the order of 10¢/kWh.  For heavier payloads, on-site pulsed power is used.  Several of the technologies used or being developed for grid energy storage, such as batteries and flywheels, are suitable for the beam director site.  For these technologies, the amortized cost adds < 3¢/kWh to the electricity cost (Viswanathan, Kintner-Meyer et al. 2013).   Capital cost is on the order of 1 $/Watt.  In comparison, the capital cost of a solid-state microwave source is 0.5-10 $/Watt, and the capital cost of a millimeter-wave source (i.e. a gyrotron) including its power supply and supporting equipment is around 5 $/Watt.  Costs will be reduced by further R&D and/or as production quantities increase.

IS PLASMADYNAMIC BREAKDOWN A PROBLEM?

At very high beam intensities, the atmosphere breaks down into a plasma, and this type of intensity limit was shown to be orders of magnitude greater than that needed for small satellite launchers (Parkin 2006).  It is possible to approach this limit with very heavy payload rockets, but this is not really a limit either, as it is always possible to flatten the rocket and increase the receiving area to keep the beam intensity well below the breakdown threshold.

HOW IS THE ROCKET AND PAYLOAD SHIELDED FROM THE BEAM?

By metal foil.  Aluminum kitchen foil is easily thick enough, and there are standard techniques to ensure that microwaves don’t propagate through holes or along any external cables or tubes through to the payload.

WHAT IF A BIRD/PLANE FLIES INTO THE BEAM?

Beam directors are located at arid, high altitude sites in controlled airspace where there are few birds.  If a bird flew just above the beam director during operation, the power density it would experience is 1,000 times lower than at the rocket, which is well above the altitudes of birds and planes.  The bird would initially experience a growing sensation of heat on its underside, somewhat like opening an oven door, and would flee, it is hoped, in a different direction.  The vicinity of the beam is monitored by radar, particularly objects that are capable of intercepting it within the duration of an ascent trajectory (3-6 minutes).  If something is about to enter the beam, it can dodge, dim, or douse (Dickinson 1978) until the obstacle is clear, or it could hand over to a nearby unobstructed beam director.  Migrating birds can achieve remarkable altitudes, and the North American flyways are quite well documented.  Research on bird radar systems (King 2013) has resulted in commercially available solutions that are capable of the kind of short-range tracking needed, such as the Merlin Avian Radar System offered by DeTect Inc.

WHAT IS THE BEST PROPELLANT?

Ammonia and methane are best and exceed the performance of LH2.  Methane is of greatest interest because it is nontoxic and soot formed by its thermal decomposition can potentially be used as a microwave absorber to post-heat the propellant to the melting point of carbon.  Water performs lower but is still a viable propellant.

HOW HOT DOES THE HEAT EXCHANGER NEED TO BE?

Hotter than 1,500 K for slush ammonia or methane.  Hotter than 2,000 K for slush hydrogen.  Hotter than 2,500 K for liquid water.

CAN SUNLIGHT BE USED INSTEAD OF MICROWAVES?

Not to launch rockets.

Similar to laser or microwave beams, longer distances require larger dishes due to the effect of optical diffraction.  However, sunlight is only partially coherent (unlike lasers and masers), so regardless of the actual size of the reflector used, it behaves as if it was coherent light emitted from a reflector that is only 70 microns in diameter.  It is possible to show that at a distance of 350 km, as would be needed for launching rockets to orbit, such a beam spreads out to a spot size that is 6 km in diameter.  It turns out that 350 km was the altitude of the Znamya 2 Space Mirror, and its spot size (projected onto the Earth) was reported to be 5 km wide.

The spot size is massively larger than the rocket!  This of course spills almost all of the energy from the beam, making it economically a bad idea.  For a target that is 1 meter in diameter, a distance of 57 meters should give an energy transmission efficiency of 86%.  Consequently, sunlight might be useful for close-range ideas but is unsuitable for long distance transmission to a small distant target like a rocket.