Traditional Aerobraking and Aerocapture
One of the challenges of orbital mechanics is that it takes just as much energy to descend into a gravity well as it does to ascend out of it. One technique that has been used for lowering the propellant cost of descent into the gravity well of a planet with an atmosphere is aerobraking. Aerobraking is the process of taking a spacecraft in an ellpitical orbit around a planet with an atmosphere, and using atmospheric drag at the lowest altitude portion of its trajectory to slowly decrease the altitude of the high end of the elliptical orbit. This process has been used now on about a half-dozen planetary missions, in some cases reducing the propulsion requirements by 1km/s or more, over the course of a couple hundred passes. Aerobraking has been traditionally been done by satellites that aren’t explicitly shaped like a reentry vehicle–in fact most of the drag for typical aerobraking vehicles is produced by using the spacecraft’s solar panels as massive drag brakes!

Artist's Impression of MRO Aerobraking (credit JPL and Wikipedia)

A more aggressive maneuver called aerocapture takes a spacecraft in a hyperbolic (interplanetary) orbit and in a single pass decelerates that vehicle into an elliptical orbit around a planetary body.  Typically the term refers to maneuvers where the ending orbit has an apoasis near the altitude of a circular orbit, though it could also be used to describe a maneuver that uses a single pass through the atmosphere to replace the “capture braking burn” that would normally be used. Aerocapture is a lot more challenging, since the deceleration has to take place a lot lower in the atmosphere in order to provide the required deceleration in such a short distance. This implies much higher forces and heat-fluxes, which require some sort of aeroshield/TPS system.

Here are a few of the main challenges of aerobraking and aerocapture:

1. Dynamic Pressure Loads: Dynamic pressure is the pressure felt on the vehicle by the impingement of the atmospheric molecules.  The equation for dynamic pressure is q = 1/2 * rho * V^2, where lower case q is the dynamic pressure, rho is the instantaneous atmospheric density, and V is the instantaneous relative velocity.  For MRO, the dynamic pressure limits were set at 0.35 Pascals, which correlates to moving at about .76m/s at sea level (ie a slow walking pace).  To give you an idea of how this compares with orbital reentrythe peak dynamic pressure of say a Soyuz in its emergency ballistic reentry mode, is over 40,000 Pa of dynamic pressure, and even a low-G lifting reentry is still in the 10kPa+ range.  Direct entry into the Venusian atmosphere from a hyperbolic interplanetary orbit gets you into the 1MPa range!  Another fun comparison is that the max-Q Xombie or Xoie have seen in flight was around 250Pa.Most of the very low allowable dynamic pressure load for past aerobraking efforts has been driven by the fact that most aerobraking craft to-date have used large flimsy solar panels as their main drag structure.
2. Peak Heat Flux:  The shockwave caused by slamming into gas particles at hypersonic velocities compresses and heats the gas particles to substantial temperatures.    Heat from this shock wave is convected and radiated into the aerobraking spacecraft.  The equation for heat flux is Q = 1/2 * rho * Ch * V^3.  Capital Q is the heat flux (in W/m^2), rho and V are the same as before, and Ch is the heat transfer coefficient.  The heat transfer coefficient, I think, represents what portion of that heating goes into the vehicle itself instead of being carried off by the now quite ruffled atmospheric gas molecules who didn’t see you coming.  Yes it is confusing that dynamic pressure is lower-case q, and heat flux is capital Q.Once again, to give you some scale, the worst case pass for Odyssey had an estimated heat flux of about 500 W/m^2,  which is about 40% of the heat you get in LEO from the solar radiation. For that Soyuz reentry case mentioned earlier, the total heat generated at max-q is in the 240 MW/m^2 range–several times higher than the heat flux at the throat of the SSME or RD-180.  The Venusian direct entry example according to one source would actually be in the 4000MW/m^2 range! Fortunately, I think that for atmospheric reentry the Ch term is relatively low–most of that heat gets carried away by the atmosphere.As with dynamic pressure loads, the reason why peak heating rates are kept so low for most aerobraking missions is that you’re using the large solar panels as most of the drag surface, and they can only take so much heating before their temperatures rise to levels that could permanently degrade their performance.
3. Atmospheric Density Variations: If atmospheric density was nice, constant, and well-known, aerobraking could proceed a lot faster and in a lot fewer passes.  The problem is that at the altitudes where aerobraking takes place (100+km), the density can vary significantly over length scales as small as 20km.  This can be driven by many processes including variations in the solar wind and solar radiation due to sun cycles, weather effects like dust storms for Mars aerobraking, and other effects.  Going off of some data from the Odyssey mission, variations as big as 2-3x were seen in density from pass to pass.   A second-order effect of density variations is that both the drag coefficient and the heat transfer coefficient will vary with atmospheric conditions by noticeable amounts.  Unfortunately,  in many cases you don’t know the density along a given trajectory in advance, so you have to plan for not the average density, but the worst case pass density.   Which means that most of the time you’re getting less deceleration and heating than you could actually withstand, but some of the times you might actually find yourself pushing your limits more than you would like.   This drives you to taking more passes than you’d really like to take in an ideal situation.  These variations get more and more pronounced at higher aerobraking altitudes, where atmospheric density is measured in kilograms per cubic kilometer.Once again, this is an area where using large, sensitive solar panels as your drag devices really hurts. Because you can’t stand high dynamic pressures or heat fluxes, you have to do your passes higher up in the atmosphere. But due to variability in density at those higher altitudes, you end up getting driven even further up to deal with worst case variations. That said, even aerocapture trajectories are high enough altitude that atmospheric variations can be important challenges to deal with.
4. Aerobraking Duration: For most previous Mars and Venus aerobraking missions, velocity changes in the 1-1.2km/s range have taken between 70-150 days, over several hundred passes.  While this is fine for unmanned missions, it’s harder to do for manned missions, where radiation concerns make you want to minimize your time spent in-transit.  The large number of cycles is also a difficulty for missions aerobraking at earth, where each pass will take you through the Van Allen belts.  Lastly, for reusable in-space transports, the total turn-time is an important economic parameter–the more missions you can fly in the same period of time, the fewer vehicles you need to support a given mass throughput.

A couple more quick observations before we jump into using MHD forces to enhance aerobraking:

• For typical aerobraking, the parameter you can control easiest is the periapsis altitude, and thus indirectly the average density.  In other words, if you want to double the drag on a pass, you lower your periapsis to an altitude that has about double the average density.  This also means that to a first order approximation (ie ignoring the relation between density and the heat transfer coefficient) heat flux for traditional aerobraking is going to scale fairly linearly with drag.
• Ballistic coefficient ends up being really important for aerobraking as well–this is the whole reason why the solar panels are used unstowed for aerobraking.  Higher ballistic coefficients mean that you have to dip lower into the atmosphere (and thus get a higher heat flux) to get the same amount of deceleration per pass.
• In spite of the disadvantages of using solar panels as your drag brakes, there are some real advantages to being able to use a aerobraking scheme that doesn’t require your vehicle to be explicitly crammed into a typically reentry-vehicle shape behind a massive heat shield.  It would be nice for instance to be able to get tanker vehicles or orbital tugs back from lunar trajectories or martian trajectories without them having to carry a big aerobraking shield like you see in all the old literature.

Anyhow, that was a quick introduction to aerobraking by a complete non-expert.

Some Backstory on Why I’m Interested in Aerobraking
I started looking into this a few months ago as an alternative to propulsive retrobraking for Centaur-derived cislunar tanker vehicles.  While a Centaur stage actually can do a lunar round trip fully propulsively, with at least some payload delivered to the Moon, the “gearing ratio” (initial mass in LEO compared to payload delivered to LUNO or the Lunar Surface) was pretty pathetic.  Just to use some ballpark numbers, without digging up my more precise calculations, I’m getting around 8000lbs payload to LUNO if you drop it off in orbit and the Centaur only returns to earth, dropping to only 2500lb if the Centaur has to haul the payload all the way there and all the way back propulsively.  However, if you could do 3km/s worth of aerobraking (assuming about 1200m/s worth of burns between the Trans-Earth Injection burn and any periapsis raising maneuvers, including the final circularization), all of the sudden you’re talking about almost 20,000lb of payload on the dropoff mission, and about 13000lb on the round-trip maneuver.  Depending on how massive and expensive the aerobraking system weighs, it makes a massive difference in the performance of a reusable cis-lunar architecture.  For a long time though, I had sort of dismissed aerobraking, because any aeroshield big enough to allow single-pass aerobraking (or few enough passes to be interesting) also ended up looking like it would either be very heavy, or very bulky, or require lots of orbital assembly or some sort of new deployable technology.  Not that any of those other than being too heavy was a total show-stopper, but it definitely made it less attractive for a near-term commercial operation.

Another line of thought I had been wondering about recently was manned cislunar transportation, especially in light of the Augustine Committee report.  One of the big suggestions they made that rubbed a lot of HLV-advocates wrong was the idea of launching the crew on commercial LEO taxi vehicles, and flying Orion up to LEO unmanned.  A lot of people said this was just silly–if you’re launching Orion may as well launch it manned, even though this would require adding launch escape and emergency detection capabilities to the HLV.  I started thinking down the lines of what Orion could look like if it was designed from the start not to carry astronauts until they got to space.  The LAS would go away, as would all the structural requirements for taking those sorts of loads, being able to rapidly drop the service module, etc.  The whole thing could fit inside a fairing, thus simplifying aerodynamics and loads on the front end of Orion.  Heck, it could even be attached to the rest of the stack in whatever orientation made the most sense for mission ops–it wouldn’t be constrained by needing to be on the top in an orientation where the capsule could “get out of Dodge” in a hurry if something “went south” with the HLV.  The more I thought about it, the more I realized that Orion could end up looking like a drastically different vehicle if it was optimized for in-space use and reentry instead of needing to also handle manned ascent to orbit as well.  Then I made an interesting leap of logic.  What if Orion was only meant to be used in space?  I originally sort of dismissed this, since most single-pass aerobraking schemes I knew of would require the thing to be designed like a reentry capsule anyway.

Jumping back to the Centaur-based tug idea, I toyed around with the idea of doing a blog series, seeing if I could make an aerobraking simulator to figure out if a Centaur could without any sort of fancy aerobraking shield actually do a multi-pass aerobraking mission that would get it back to LEO within a reasonable amount of time (say three weeks or less).  However, I stumbled on the papers about magnetic aerobraking right about this point in my thought process, which may possibly provide a solution to both of these problems.

While I don’t have anywhere near the analytical chops to know for sure how far you can push this technology, if it could enable single-pass or at least small number of pass aerobraking without requiring a huge traditional aerobraking shield, interesting things might become possible. Magnetic aerobraking could potentially revolutionize cislunar transportation, enabling low-cost reusable manned and unmanned deliveries based on modified versions of existing LOX/LH2 upper stages, and could allow fully-reusable in-space only manned vehicles that weren’t just an overglorified 1960s-style reentry capsules.  But more on that later.

For now let’s get back to how we can use magneto-hydrodynamic interactions to enhance traditional aerobraking, and see if we can figure out if this idea has merit at all.

Magnetic Aerobraking
Going back to our previous two discussions, one of the key takeaways was that the enhanced braking and thermal protection provided by strong magnetic fields was strongest at high altitudes where atmospheric density was lowest. At high altitudes, the ambient atmospheric density is low, but Joule heating caused by the interactions between ions in the shock layer and the superconducting magnet keeps the electrical conductivity of the plasma in the shock layer high. Also, for aerobraking or aerocapture short of reentry, by definition you are both always at a speed and altitude high enough that you don’t have to worry about the shock layer losing sufficient conductivity for MHD effects to dominate aerodynamic drag effects. The magnetic interaction parameter (Qmhd) introduced in my first post in this series can easily be in the 250-1000+ range at high altitudes compared to down in the 5-50 range you might see during atmospheric reentry. For example, the paper I cited in my first article (Otsu et al) showed that for a vehicle coming back from a GTO-like orbit, you could cut the return time by 70% with a 0.1T magnet, which is about 5x weaker than the magnet assumed for most of the reentry magnetic TPS studies.   While magnetic effects may be helpful for reentry, they truly come into their own for aerobraking and aerocapture.

A few other thoughts:

• While the total drag for a magnetic aerobraking concept can actually be several times the drag of a similar non-magnetic vehicle, the gas-dynamic portion of the total drag actually decreases substantially in the case of magnetic aerobraking.  This is due to a much lower velocity behind the shock layer in the magnetic case.  Figure 9 from the Fujino et al paper I used in the last post (“Numerical Analysis of Reentry Trajectory Coupled with Magnetohydrodynamics Flow Control”, JS&R Vol 45 No 5, pg 911-920) illustrates this beautifully:
• For a vehicle using magnetic braking, most of the total drag force is actually reacted electromagnetically through the magnet itself, not through the surface of the vehicle.  The dynamic pressure that the vehicle surface itself sees is greatly reduced compared to what you would expect at that altitude and entry velocity.
• While in the above case, the dynamic pressure reduction was about 4x at ~75km, this effect is likely to be even more pronounced at the altitudes used for aerobraking (90-120km) where the electromagnetic interaction parameter is substantially higher (40-160x higher) than it is in the case shown above for atmospheric reentry.
• The heat flux seen by the aerobraking vehicle will also be greatly reduced compared to a non-magnetic aerobraking system at a similar altitude and velocity.  This is due to the much thicker shock layer standoff distance and the lower velocity of the particles behind the shock layer.  The Fujino et al paper estimated that the heat flux would roughly be cut in half at 75km with a 0.5T magnet (due to a boundary layer between the bow shock that is twice as thick at that magnetic interaction parameter).
• For higher parameters in the 100-1000 range that you would likely see for aerobraking, this effect should be even more pronounced.  The trend in shocklayer thickness vs. Qmhd shown in Fig 3 of Fujino et al  was linear over the Qmhd range of 0-6.  If it continued out linearly up into the Qmhd 100-1000 range, the shock layer standoff distance would be in the range of 100-125x thicker than without MHD effects, implying a drastically reduced heat flux at aerobraking altitudes.  Unfortunately without having them run the actual analysis, it would be hard to know precisely how well this would work.
• All these factors mean that the same vehicle could use a lower periapsis with a magnetic braking system than without.  The dynamic pressure and heat flux that the vehicle sees at a given periapsis altitude is going to be at least 2-4x and possibly more than an order of magnitude less than it would be without the magnetic field.  Even in the most conservative case (ie assuming that the effect at 100km and aerobraking speeds is no better than at 75km in spite of having a Q 40-160x higher) this would allow you to go to an altitude with at least double the density while keeping the heat flux and dynamic pressure loads within tolerances.  With an effective total drag 4x higher at a given altitude combined with being able to go to a lower periapsis, you get bare minimum a 8x reduction in total aerobraking time compared to the non-magnetic case.
• For the aggressive, “I don’t know if I’m extrapolating way too far” case, you could get even larger reductions in aerobraking time.  Going back to my linear extrapolation on shock layer standoff vs. Qmhd (and thus heat flux vs Qmhd), at Qmhd=250 this would put the shock layer standoff at about 25-30x thicker than the non-MHD case.  The example in Otsu et al gave a Qmhd of 250 using a 0.1T magnet and a 100km periapsis.  Since Qmhd is proportional to B^2 and inversely proportional to rho.  If you increased the magnetic field from 0.1 to 0.5T (similar to what was being suggested for the reentry studies done by Fujino et al and some of the others), you could maintain a Qmhd of 250 even if you increased the local density by a factor of 25.  At Qmhd of 250, the effective drag coefficient is about 3x higher than the non magnetic version.  That would give up to a 75x reduction in aerobraking time compared to the non-magnetic case.
• One other advantage of magnetic aerobraking is that you can drastically vary your effective drag coefficient electrically.  Also, the heating and dynamic pressure are far more driven by the magnetic field strength than by the atmospheric density for the MHD aerobraking case.  These mean that you can afford to take deeper passes without having to worry as much about variability.  If the density is higher than expected, and you have some head-room on your magnet, you can increase the MHD field strength a bit to keep the shock layer back and the dynamic pressure down.  This also could cut trip times in half just by allowing you to base your planning off of the average atmospheric density instead of having to take the mean + 3 standard deviations as your predicted atmospheric density.

I’m rapidly coming up to the point where I’m pretty sure I no longer know what I’m talking about.  At least from here, it looks like there’s a good chance that MHD aerobraking could allow for aerocapture (at least into a high eccentricity elliptical orbit), and very rapid aerobraking down to a circular orbit compared to the non-magnetic case. I think you can extrapolate the conclusions of these papers in these ways, but without having the people with the analysis tools actually verify these claims, I’d still take them with the appropriate sized grain of salt.   Also, my intuition on how a MHD aerobraking vehicle would compensate for density variations is not very good.  That alone could be a paper or a thesis.

So, whether this ends up being a mild curiosity that ends up only being useful in niche applications, or a game-change remains to be seen, but the potential for this being a game-change is real.

In my last post in this series, I’ll go more into some of the implications of what this could do if it works, and some thoughts on how to actually flight-demonstrate MHD aerobraking.

[Edit: It turns out I had misspelled Fujino's name in the original post. Fixed that and added the title of the paper in case people want to get a copy--it's free if you have a JS&R subscription, $15 if you're an AIAA member without a JS&R subscription, and something like $30 if you're not an AIAA member--highly recommended if you're interested in this topic]

RLV Thermal Protection Systems
Protection from the harsh heating environment caused by atmospheric reentry is one of the biggest challenges for reusable vehicles–far more difficult than the often harped-on rocket equation or the “inefficiency of chemical propulsion”. The problem isn’t even the weight of the thermal protection system as much as it is the maintenance requirements. Ideally you’d like a TPS solution that requires very little maintenance, and can be “tested” easily and quickly on the ground before flight, even if it cost you a little extra weight. You’d also prefer something that was relatively simple operationally to use, with a minimum number of failure modes. MHD thermal protection seems like an interesting match for these requirements. I should note however that there are other promising ideas out there such as transpiration cooling that might also work on their own or in combination with MHD thermal protection, but they are beyond the scope of this blog post.

Some Take-Aways from the Literature on MHD Reentry TPS
There have been several interesting papers on this topic, including the JS&R article “Experiment on Drag Enhancement for a Blunt Body with Electrodynamic Heat Shield” that got me thinking about this more seriously, a second JS&R article that goes into experimental proof of the heat flux reduction “Experimental Verification of Heat-Flux Mitigation by Electromagnetic Fields in Partially-Ionized-Argon Flows”, and another JS&R article from a year and a half ago “Numerical Analysis of Reentry Trajectory Coupled with Magnetohydrodynamics Flow Control” that I’ll be leaning on pretty heavily for this discussion. You can purchase the articles from AIAA, or if you already have a subscription to the Journal of Spacecraft and Rockets, you can read them for free.

I’ll briefly summarize some of my takeaways before going into my thoughts on how to move things forward from there:

1. Both analytically and experimentally, magnetic reentry TPS appears to provide large reductions in both peak heating and in total heat load.  The third paper above suggested a 30% reduction in peak heat load and a 40% reduction in total heat load for ballistic reentries.  Under the conditions tested in the second paper, heat reductions up to 85% were shown.
2. The magnetic braking effects dominate aerodynamic braking effects at high altitudes.  This is mostly due to lower density meaning that atmospheric drag is fairly low, while also lower density means that Joule heating caused by the currents (the loop marked “J” in the previous post) induced by the magnetic fields increases the electrical conductivity more effectively than at lower altitudes.
3. The more deceleration that can be done high up in the atmosphere, the lower the peak heating and the lower the total heat load.  The heat flux is roughly proportional to the cube of the velocity.
4. The heat flux reduction from this scheme is dominated by the increased shock layer thickness at high altitudes, and at lower altitudes is dominated by the much lower velocity by the time you get there by getting extra braking high up.
5. Conductivity of the plasma is one of the keys to making this work.  The conductivity in these cases was entirely due to the temperature in the plasma–higher velocities lead to higher temperatures, and Joule heating also leads to higher temperatures.  As velocities slow down, conductivity drops, as does the effectiveness of the braking system.  Below about Mach 12, the only way to keep the flow ionized enough to control magnetically is to add energy via some mechanism.
6. Because of the large induced currents, this idea only works if the heat shield is an electrical insulator.  If it is a conductor, you’ll just generate hall currents in the heat shield which will null out a lot of the benefit of the approach.

Thoughts on Maximizing the Effectiveness of MHD Reentry TPS
Based on these takeaways, and the discussion in the last post, I’ve come up with a few ideas for how to maximize the effectiveness of an MHD heat shield.

1. Use a lifting reentry.  Just as it is possible to offset the CG of a reentry body to generate some aerodynamic lift, it may also be possible to locate and orient the magnet in a way to create both lift and drag.  If you do a force balance on a body in a circular orbit, the downward gravitational force is exactly balanced out by a fictitious centrifugal force due to your forward velocity.  As you decelerate though, that centrifugal force component decreases, but by using lift, you can counteract some of that gravitational force.  This allows you to stay up at a higher altitude longer, which allows you to do more of your deceleration in the lower density air.  This is already used by all manned space capsules as well as the shuttle in order to keep reentry decelerations to a reasonably low level, and also to reduce the peak heating.  This is even more beneficial for magnetic braking concepts, because you can do more of your deceleration at a point where the magnetic effects dominate, electrical conductivities are high, and heat fluxes are low.
2. Use as strong of a magnet as you can reasonably work with.  While there are diminishing returns according to all of these papers, a stronger magnet does help provide more deceleration and shoves the boundary layer away further.
3. Use an alkali seed.  As velocities decrease, it gets harder and harder to maintain the electrical conductivity in the plasma at a high enough value to maintain useful levels of Lorentz interaction.  This is similar to the challenge with MHD electric generators.  In order to keep the conductivity high, injecting an alkali metal into the stream can help.  Alkali metals, particularly Potassium and Cesium have very low ionization energies compared to air.  In a weakly ionized plasma, most of the atoms are actually not atomized–almost all of the conductivity is provided by the small number of atoms that are.  So, a little bit of seeding can go a long way.  This helps you keep your magnetic deceleration forces high even as altitude and velocity drop.  The other nice thing about seeding, is that depending on what the fluid is, it might also cut down on the radiative heat transfer from the hot shock layer back to the heat shield.
4. Heat the plasma.  This may sound counterintuitive, but you might actually get better thermal protection if you start heating the plasma once you get to a certain point.  Below Mach 12, even with seeding, there just isn’t enough heat rise caused by the shock layer to keep the plasma  sufficiently ionized.  But, it is actually possible via several different means to dump a bit of energy back into the shock layer to push the gas back into an ionized state.  It’s unclear at this point if this is worth doing, but if the system is light and simple enough it might be worth considering.  As it is, you’ll have a lot of stored energy in the superconducting magnet, and you probably want to dump that somehow before landing–using it to keep the incoming air ionized a bit longer to get a little more deceleration before you hit the thick air might be worth it.

All told, you’re still going to need some sort of thermal protection for the last bit of deceleration, but the heat loads and max temperatures are so much lower if you can dump say half the reentry velocity while you’re still high up, that the problem becomes a lot easier to deal with.  If you could only get down to Mach 12 with this system, that would cut the peak and total heat loads by at least a factor of 8x.  The heat fluxes at this point would be low enough that you wouldn’t need ablative materials, and could probably use a ceramic tough enough that it was low maintenance.

Anyhow, the key questions I have at this point are: a) what sort of effective “L/D” ratio can you get by varying the location and orientation of the magnet, b) how much does seeding help, c) how long can you stay up in the high altitudes, d) what is the maximum amount of velocity decrease you can provide via this method, e) how strong of a magnet could you reasonably hold on an RLV, f) how does the strong magnetic field interact with the operation of the RLV itself–what does it do to solenoid valves, electric actuators, etc. and is there a way to shield against these issues?

In the next segments, I’m going to talk about another, possibly even more interesting application of this concept, as well as some thoughts on how we can reduce this technology to practice.

Oh, and one small caveat before I jump in–while I think there’s some real potential here, electromagnetics is a topic that I’m truly awful at. I’ve never had another class, including a PhD level turbulent fluid dynamics class that made me feel like such a brow-dragging neanderthal as my Physics 122 class on Electromagnetism. This may be yet another niche technology that while somewhat interesting, ends up not being all that useful. But it looks at least possible that this may become a game changing technology in many space transportation fields. Without further ado, let’s go over some of the basics.

Some Background on MHD Aerobraking and Thermal Protection
The basic concept behind MHD Thermal Protection is that during hypersonic flight, above about Mach 12, the shockwave formed in front of a blunt-bodied vehicle reaches a high enough temperature to form a weakly ionized plasma that is conductive enough to be manipulated by strong magnetic fields. A powerful magnet near the leading part of the vehicle interacts with charged particles in the plasma via the Lorentz force. This force bends the trajectory of charged particles, creates large hall currents, which if I’m understanding correctly repel the magnetic field. These charged particles also impact with the uncharged gas particles nearby (the plasma is only “weakly ionized”) transmitting these forces to them as well. Here’s an interesting diagram I’ll reference from one of the papers I’ll talk about more later (“Trajectory Analysis of Electromagnetic Aerobraking Flight Based on Rarefied Flow Analysis” by Otsu, Katsurayama, and Abe–well worth the $28):

Figure 1 (from Otsu et al): Schematic View of the Flow Around a Vehicle With Applied Magnetic Field and Induced Current

If the magnet is strong enough, this leads to two interesting effects–first, the distance from the vehicle to the bow shock increases (I think the plasma density between the bow shock and the vehicle also decreases, but I’m less sure about that). This can significantly reduce the heat transferred into the vehicle for a given velocity and altitude. The other big effect is that the Lorentz forces create forces that can produce drag or lift. At high altitudes these Lorentz forces can greatly augment the aerodynamic drag forces, effectively making it as though the vehicle had a much lower ballistic coefficient. It should be noted that this force is electrically controllable. In fact, depending on the sophistication of the magnetic apparatus and its location within and orientation with respect to the vehicle, it can possibly also produce lift as well as control torques without the need for aero control surfaces.

Both of these help from a reentry thermal standpoint, because by the time you hit the denser air, where the heating is the highest, you’re going a lot slower than you would’ve been otherwise, and a lot of that earlier braking is done at much lower heating loads than would have been the case without the electromagnetic effects.

Several of the papers I’ve read introduce an interaction parameter term, Q, that relates the relative strength of the Lorentz forces to drag forces. The relationship takes the form:

Equation 1 (from Otsu et al)

Sigma is the conductivity of the weakly ionized plasma, B is the magnetic field strength, L is a reference length (I think related to the magnet configuration), rho is atmospheric density, and V is velocity. As you can see, for a given magnet, the drag forces start dominating as the conductivity drops and as the atmospheric density increases. Atmospheric density increases dramatically as you descend from orbit, so for a reentry application, you get most of your benefit from the first little bit of descent.

We’ll go more into some of these ramifications starting in my next installment.