We have designed an artificial local geomagnetic field, or magnetostatic shield, to protect a crewed Mars facility from cosmic rays. The shield is modeled after the results and suggestions of Motojima and Yanagi 2008. Modeling indicates that the shield is effective against protons to 1 GeV. The shield deflects all solar storm protons, nearly all solar flare protons, and more than half of Galactic Cosmic Ray (GCR) protons. The design applies existing technology from superconducting power lines, superconducting solenoids, and carbon nanotube (CNT) cables. The presented shield is scaled to protect a crater 9 km in diameter and 2 km deep. Power requirement is under 80 kW. The design can be scaled for larger sites. Shield effectiveness decreases by roughly 100 MeV for each 100 m decrease in vertical separation of shielding cables.
A crewed Mars facility must be protected from cosmic rays. Absent protection, most crew members would absorb a career-limiting radiation dose in the course of a single-synod mission, as inferred from McGirl et al. 2016. For this reason Mars hab designs often dump several meters of regolith dirt atop a hab, or else sequester the hab within a frozen tunnel or cavern. Surface excursions remain essentially unprotected.
The Lake Matthew Team's MATT
invention took a different approach to cosmic ray protection, heating bedrock to produce a meltwater reservoir. This enabled production of a radiation shield comprised of 5 m of treated freshwater, to protect a hab at essentially any scale.
While the MATT method gives a hab full cosmic ray protection, plus sunlight, it does not address the need for protection outside the hab itself; e.g., during construction phases, or on excursions to distant sites of scientific interest. To address this need we propose consideration of an artificial geomagnetic field. It's designed as a magnetostatic field sufficient to protect crews on the open surface. This entry's design is given at the scale of Omaha Crater, the proposed MATT facility crater, which is ~9 km in diameter and ~2 km deep. It's a scale that matches the ambition of Mars Home Planet, to protect "1 million people... living, working and moving around on Mars".
Our thanks to poster Aurora-L for pointing us to Motojima and Yanagi
2008. That paper provided many quantitative results indicating the feasibility of artificial geomagnetic shielding of a planetary surface. Our thanks also to our thoughtful reviewers, who kindly considered our preliminary results.
3-D magnetostatic FEM with charged particle tracking
The shield is tested on cosmic ray protons, as protons comprise ~90% of ionizing cosmic rays. Protons are injected vertically downward into the shield. Note that vertical protons are the hardest to deflect, as their transit time through the shielding field is briefest. For confirmation of this working assumption, low-angle protons were observed in simulation to be more easily deflected than vertical protons.
Fig. 1. Omaha Crater
MATT's notional design for Omaha Crater, with north to upper left. Crewed facilities
follow the north/south center-line. No crewed facilities are near
the east or west crater rims, where shielding field B magnitude exceeds human safety limit of 5E-4 Teslas.
Fig. 2. Primary and Return Shielding Cables
Shield-generating cables are shown. Primary shielding is provided by 5 high-temperature superconductor (HTS) unipolar power line cables. The central cable bundles 100 kA conductors, for a maximum 6.4 MA DC current, which is the notional cabling and current of Motojima and Yanagi 2008. The 5 primary shielding cables carry a combined 24.8 MA current. Shielding cables are separated at 1.25 km horizontal distance.
Primary shielding cables are the higher cables in Fig. 2, at 500 m above the pre-impact surface (rim+pylon height 500 m). Return current is carried below, on cables suspended 1 km above the crater floor.
Fig. 3. Unipolar HTS Power Line
Suggested power line cabling design, from Motojima and Yanagi 2008. HTS tape is ReBCO. The exterior vacuum hardware is designed for terrestrial atmospheric pressure and temperature; it may be simplified or reduced in mass to counter the lower pressure and lower temperature of the martian atmosphere.
Fig. 4. HTS Solenoid:
Suggested solenoid cable design, from Tomassetti et al. 2016, with photo from Minervini 2015. HTS tape is ReBCO. Solenoid design is constrained by critical current and Lorentz force, as in van der Laan 2013. Solenoid current is reduced with parallel solenoids. Lorentz force may be reduced by increasing solenoid diameter. Conceivably a lightweight inflatable solenoid shell could be designed to manage Lorentz force. Lorentz force would inflate the shell, expanding the solenoid to a diameter at which the shell hardens to counter the force. This would reduce solenoid mass by eliminating the need for a metal shell, such as steel. For a relevant prototype example, see the inflatable ReBCO shielding toroid of Porter 2016.
Fig. 5. A Shielding Circuit
Crater outline in brown. A primary shielding cable (red) is a unipolar power line that runs from the west rim to the east rim. The cable is horizontal under CNT suspension cabling. Return current (blue) on the east crater wall is self-shielded within a set of solenoids, to prevent weakening of the primary shield. Solenoids hold return-current external B magnitude below 1E-4 T on the crater wall.
Off the crater wall, return current is suspended (purple) at an elevation of 1 km above the crater floor. Here half of the current travels through a self-shielding solenoid and half travels through a unipolar power line. The half-current line opposes the primary cable's magnetic field, significantly lowering B magnitude on the crater floor. Floor B magnitude is kept below the recommended human safety limit of 5E-4 T (white).
The shield's B magnitude contours have been designed to approximate the crater floor shape, with safety limit set at an elevation 600 m above the floor. As shown in Fig. 5, the field approaches this limit 625 m off-center north (or alternately, south) of the central primary cable, a position midway between 2 cables.
On the west crater wall all return current is self-shielded in a set of solenoids (blue). On the west rim all current passes into a unipolar power line, to complete the circuit.
All cables are notionally affixed to nickel/iron ISRU
alloy pylons grounded in the crater rim and wall.
Preliminary shielding results are summarized. This is all still first-pass. It needs magnetohydrodynamic modeling for completeness, but the preliminary results have survived initial expert review.
500 MeV Shielding:
Fig. 6. 500 MeV Shielding, Overhead
Shielding effect, overhead view, 500 MeV protons.
Vertically-injected 500 MeV proton tracks in white, crater rim in red.
Nearly all 500 MeV protons are deflected away from the crater floor.
B magnitude is plotted in Fig. 6 at an elevation of 6.3 km above the crater, or 5.8 km above the shield cabling. The shield's maximum B magnitude (not shown in Fig. 6) is found only within 200 m of the center-line cable, approaching 1E-2 T.
Fig. 7. 500 MeV Shielding, Perspective
Shielding effect, perspective view, 500 MeV protons.
Vertically-injected 500 MeV proton tracks in black, crater rim in red.
Nearly all 500 MeV protons are deflected away from the crater floor.
1 GeV Shielding:
Fig. 8. 1 GeV Shielding, Overhead
Shielding effect, overhead view, 1 GeV protons. Vertically-injected
1 GeV proton tracks in white. More than half of 1 GeV protons are deflected away from the crater floor.
Fig. 9. 1 GeV Shielding, Perspective
Shielding effect, perspective view, 1 GeV protons.
Vertically-injected 1 GeV proton tracks in black.
More than half of 1 GeV protons are deflected away from the crater
Shielding Effectiveness in the Mars Environment:
Fig. 10. Shielding of Solar Flare and GCR Protons at the Martian Surface
Net shielding effect on Mars is shown, with 500 MeV and 1 GeV results marked in green
and yellow-green. Figures are from Mars cosmic ray model of Wilson et al. 2001. Protons with z = 1.
All solar storm protons are deflected. Nearly all solar flare protons are deflected. More than half of
GCR protons are deflected. This entry's design appears to provide a
robust shield, with local field B magnitude and deflection capability exceeding that
of Earth's own geomagnetic field.
The shield can be deployed at sites having less than the 1.5 km vertical cable-separation of Omaha Crater. Shielded proton energies are seen in simulation to drop roughly 100 MeV for each 100 m decrease in vertical separation of shielding cables.
We are examining a magnetostatic
shield because electrostatic
shields can't work in the martian atmosphere. The atmosphere's electrical conductivity is far too high to permit the buildup of useful electrostatic shield potential. It's roughly 2 orders of magnitude higher than Earth's atmospheric conductivity, per Harrison et al. 2016. On Mars an electrostatic shield would suffer continual electrical discharge, which prevents operation.
HTS ReBCO cabling is used to minimize superconductor refrigeration power requirement. The design requires ~100 km of refrigerated cabling. The superconductor has no losses, with exception of joule heating in joints, which are minimized in the all-ReBCO circuit design. The greatest power requirement is that for replenishment of the LN2 or LOX boil-off, and pressurization. Terrestrial refrigeration requirement is roughly 1 W/m. The extremely cold martian environment eases refrigeration requirement (one easy thing on Mars), so the power requirement might be somewhere between 30 and 80 kW. This is a modest requirement, especially for a facility where some tens of MW must be generated, if only to manufacture sufficient propellant for the crew's Earth-return flights.
A solenoid's self-shielding configuration lowers external B magnitude while increasing internal B magnitude. This prevents unwanted reduction of the primary shielding field's B magnitude above the crater walls. To illustrate the effect:
Fig. 11. Solenoid on East Crater Wall
Fig. 11 isolates the central return cable on the east wall (blue diagonal line at
right). It carries 6.4 MA return current, as a solenoid.
Fig. 12. Solenoid External B Magnitude
The solenoid's B magnitude is plotted in Fig. 12 at 125 m off the solenoid
Note that appreciable magnetic fields are present only at the ends of
the solenoid, at a scale of 1E-4 T at 500 m distance.
solenoid ends the B magnitude drops to 1E-5 T range, which is below the
maximum desirable value of 1E-4 T. The solenoid therefore
lowers the return cable's external B magnitude to a value that does not
significantly reduce the shielding field's effectiveness.
Alternate Self-shielding and Source-shielding:
Solenoids self-shield the first and last 2 km of return-cabling. However other self-shielding and source-shielding options are conceivable. One of these options might be chosen if a future evaluation judges it superior in some critical respect. 3 options are considered:
Metal piping for source-shielding:
In this option half the current returns outside the crater. The other half returns inside the crater. An iron pipe contains and source-shields the unipolar return cables on the crater wall. The pipe is removed only where cables are suspended 1 km above the crater floor.
For this purpose an ISRU iron smelting facility must be capable of producing iron pipe segments from global unit dust or other surface iron source. Piping might exceed 1 m in thickness.
This simple iron source-shield might be augmented. For example Cryoperm shielding is especially effective at cryogenic temperatures, which are close to the temperatures encountered in winter. However all shielding materials have magnetic saturation points and other physical limitations. Determination of the optimum metallic source-shielding combination would require considerable analysis.
Voltage conversion for self-shielding:
If an ultra-high-efficiency voltage
converter could be implemented (notionally >99.9% efficiency), current in the cables (and B magnitude) could be increased or decreased with a corresponding voltage change. On the east rim voltage would be raised, to lower the return current and B magnitude. This
ultra-high-voltage DC (UHVDC) current would travel down the east wall. At 1 km altitude another
converter would lower voltage to 2x the primary cable's voltage.
This would produce the required half-current return above the crater floor. On the west wall voltage would
be raised again, and the UHVDC current would return to the west rim with low B. On
the west rim the voltage would be lowered once more, to match the
primary cable voltage and complete the circuit.
However this method would only be
feasible with ultra-high-efficiency voltage converters, which might not
be achievable. Any appreciable inefficiency would require excessive power for maintenance of the 24.8 MA of total shield currents.
Bipolar cable self-shielding:
In a bipolar cable, B magnitude is reduced to micro-Teslas by running opposite polarities together; that is, integrating return current into the same cabling that houses the primary current. Where implemented, no external shielding metal is required in order to eliminate the external magnetic field.
Fig. 13. Bipolar HTS Cable
Image from Stemmle et al. 2012. Bipolar cabling might not be applicable to a shield
design because long stretches of cable must be unipolar in order to
produce a shielding field at multi-km distance. But if some clever way
were found to incorporate bipolar cabling into the design, without
violating circuit laws or getting into a diminishing-return scenario, bipolar cabling would be a mass-efficient way to manage B magnitude. We just don't see how it could be done
in this particular facility.
Fig. 14. Effect of Bipolar Source-shielding
Image from Stemmle et al. 2012. Residual B
magnitude is on the order of micro-Teslas near the bipolar cable.
Rim Transit and Field Safety:
In this design the northern and southern crater rims encounter field B magnitude of 7E-4, which is slightly higher than the safety limit of 5E-4. However these rim sites are only infrequently transited, not inhabited. Moreover any vehicles transiting these sites will contain some metal plating that acts as subject-shield. Even mm plating should lower the interior B magnitude below 5E-4. (This limit is environment-safe, for crews among equipment with magnetic susceptibility. The medical limit is higher. The UK National Radiological Protection Board (NRPB) sets the field exposure limit at 0.2 T when averaged over an 8-hour working day (Schenck 2000). This medical limit is readily maintained throughout the shielded facility, even in close range of shielding equipment.)
Launch and Landing:
Transiting spacecraft pass through field regions with B magnitude approaching 1E-3 T. If this presents a risk, the shield current can be shunted temporarily to a set of superconducting magnetic energy storage (SMES) units. This turns the shield off during transit. After transit, the SMES units discharge to turn the shield back on. SMES charge/discharge cycles have ~95% efficiency, so some days of additional recharge, or a supplemental SMES unit, would be required to fully restore the current and shield.
Also, a point of terminology: "turning the shield off and on" seems incorrect. A shield should be "lowered and raised". Also one feels need for a klaxon
One tries to imagine how such a high-wire facility would appear
, under actual operating conditions; but perhaps only professional artists can really imagine it. Here midair circuits glow with corona discharge. On winter mornings dry ice sublimates off CNT suspension cables, as repair bots patch the fiber. 3 km below the dangling bots, Lake Matthew is a shattered blue pendant. Above the bots, magnetic particles abandon dust storms and dust devils to spiral off into the shielding field. And during solar storms, would the east and west rims experience... aurorae?
Here as elsewhere, the Lake Matthew Team is keenly aware of its artistic limitations. Maybe some MHP artists would like to give the entry's more dramatic aspects a bit of pro imagination.
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