Habitable environment on a big moon of a gas giant lacking magnetosphere

I am trying to figure out how to make a moon (75% of Earth size) of a gas giant habitable.

To give an idea of the technological level, here are technologies the colonists have access to:

• fully automated and robotised asteroid mining;
• space travel at 1/10 of the speed of light;
• terraforming technologies (however, only one project has been completed successfully by the time of their departure);
• genetic engineering;
• suspended animation.

Some details of the planetary system chosen for colonisation:

• K-type main sequence star (about 60% of Sun size);
• large asteroid belt which can be mined for all and any necessary materials;
• there is a gas giant in the Goldilocks zone;
• this gas giant does not have a strong magnetosphere;
• it has 3 moons, the largest of which is being colonised;
• this moon is the only candidate in the entire star system for establishing a colony.

The colonists do not have contact with Earth and cannot receive supplies or technology updates. The majority of them are scientists (not just STEM, social sciences as well) and engineers. The team is very small — under 200 people. At the time of arrival at the system, almost all fuel is exhausted. While, theoretically, it is possible to set up fuel production in the asteroid belt, refuel the spaceship and look for a more inviting place, the colonists decide to stay.

The moon chosen for terraforming is very much a dead rock. There is no water, atmosphere, or life. It is a perfect blank canvas for the project. However, it does not have a magnetosphere. So, there is a huge concern that the solar radiation will strip their new home of artificial atmosphere and damage organic life.

Is it possible to create an artificial magnetosphere? How can it be done?

• The "huge concern that the solar radiation will strip their new home of artificial atmosphere" is misplaced; while the effect is real, it works in geological time, that is, over millions of years, not in human-civilization-scale time. On the time scale of a human civilization, that is, thousands of years at best, the solar wind eroding the atmosphere is a non-issue. – AlexP Aug 26 '17 at 9:40
• If the Gas Giant would have magnethospehere, the situation would be probably even worse. The radiation belts of Jupiter make the surface of Europa almost inhabitable. (with spacesuit.) – b.Lorenz Aug 26 '17 at 11:19

You do not need a magnetosphere

Theory

Kass and Yung, 1995 have one of the higher estimates of atmospheric sputtering (removal of gasses from the atmosphere through interaction with the solar wind) from Mars. Their work deals with loss of oxygen from Mars. For all sources of oxygen (diatomic, carbon dioxide, and water), particulate loss rate on a young Mars with a thick atmosphere is estimated to be about $4\times10^{28}$ particles. Multiplying by the mass of each particle, this works out to about 1500 kg of atmosphere per second.

This may seem like a lot but it really isn't. Lets say your planet has an atmosphere 1/10 the mass of Earth's (if it is smaller and thinner). The atmosphere is then about $5\times10^{17}$ kg. To remove 1% of this thinner atmosphere (or $5\times10^{15}$ kg) at 1500 kg/s would take 100,000 years.

Certainly, on the time scales of planets this is a big deal. But for humans? Not so much. If you have the ability to add a whole atmosphere in a few centuries, surely it isn't to hard to replace 1% of your atmosphere every thousand centuries.

Application

This one is easy. Behold Titan, moon of Saturn. Titan is the only known moon with a significant atmosphere (surely of interest to the potential moon-colonizer). It also has no magnetosphere, and its parent planet Saturn is not nearly as magnetically potent as Jupiter. Finally, it is also tiny; its mass is 2.3% of Earth's and its surface gravity is 14% of Earth's.

Yet, it has a dense nitrogen atmosphere with a mass 1.2 times that of Earth's. Certainly Titan has less solar wind to deal with than Earth, but nonetheless it maintains has maintained a thick atmosphere for billions of years after its creation with only a fraction of the surface gravity of Earth.

Regarding solar wind, Venus is also here. It is closer to the sun and gets more solar wind. Despite having no magnetosphere, it still has a super dense carbon dioxide atmosphere almost 100 times more massive than Earth's.

Conclusion

Worst case scenario, you have to spend some time and money repairing your atmosphere every few millenia. Best case, you find one of the myriad reasons that atmospheres are protected; i.e. whatever it is that is protecting the atmospheres of Venus and Titan.

I have no doubt that your magnetosphere-less moon's atmosphere will be removed over geological time (a few billion years), but your sun is also going to expand into a red giant in a similar time span, so lets worry about first thing first.

• What about radiation? AlexP was kind to mention that atmosphere loss will be negligible and your answer provides a well-supported proof for it. But I am still concerned about radiation protection. (And building an artificial magnetosphere seems to be a good plot element :).) – Olga Dec 27 '17 at 16:53
• Venus has an induced magentosphere protecting the bulk of the planet. It isn't strong enough to prevent solar wind penetration on the subsolar face, so lighter gases (H, HE, O) have been stripped away leaving heavier compounds in great density. – rek Jan 9 '18 at 16:51

You may be interested in this article, which is about enhancing Earth own magnetosphere, but can obviously be applied to any other celestial body.

It has a lot if information and is a recommended reading; here is an Executive Summary (for the part of interest):

• building a magnetosphere for a planet by putting magnets on planet itself is inefficient.
• to protect a planet from solar wind/flares it may suffice a smaller shield in L1 (Lagrange Point 1, which is a unstable orbit between sun and planet).
• Shield must be kept in position by active (ion?) motors because of instability; needed push is very low.
• Shield should have a magnetic field charge level from 1 and 2 Tesla depending on desired coverage.
• Energy to maintain the shield can be directly extracted via solar panels (no need for autonomous generators).

This study has been adapted by NASA for a proposal for a Mars shield.

In Your case having the shield in L1 of the satellite wouldn't help, of course, so it should be in L1 of the planet and large enough to protect gas giant and bodies orbiting it.

It may be necessary to step up magnetic field to cover a larger area, but if this is something NASA is actually evaluating now it should be a no-brainier for any race able to build starships.

science.nasa.gov:

"Earth's magnetosphere is part of a dynamic, interconnected system that responds to solar, planetary, and interstellar conditions. It is generated by the convective motion of charged, molten iron, far below the surface in Earth's outer core."

So in theory to have a magnetosphere you need a huge amount of charged molten iron. Conventionally, this is impossible to generate because the quantities of iron are on a planetary scale, difficult to obtain, as with your situation, core mining other planets and moons in the solar system would require too many resources.

However, if we are talking fully automated and robotized mining, theoretically they could mine asteroids for iron, provided there are enough iron rich asteroids in the system, the quantities in question are still very large and would require a shaft to the core of the planet, which at the given technological level would be a little difficult.

Alternatively, if vacuum energy is a thing that they have, one could go with an extremely strong electromagnet, at the surface or the center of the planet. Vacuum energy, however might again, be a bit out of the technological reach of our colonists and if it was on the surface of the planet it would severely interfere with any sort of un-shielded electronic equipment.

So, in reality, for a small team of scientists at the level of tech described, it'd be pretty darn difficult to pull a feat like that off. It would take a more advanced civilization years to gather the necessary iron and to create the conditions for a magnetosphere to be created. Without significantly more advanced tech, or the resources of a whole civilization, im afraid you'll have to look for a new planet, or simply shield your shelter from radiation. That'd probably be a lot easier than creating a magnetosphere.

On the other hand, today we are already discussing mars' magnetosphere and some info can be found here: https://www.hou.usra.edu/meetings/V2050/pdf/8250.pdf