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Noclevername
2013-Oct-05, 01:10 PM
In a vessel moving at relativistic speeds, how strong would a mini-magnetosphere have to be to protect a manned section against cosmic rays, let's say if you are going at 50%c, 80%c, or 99%c.

antoniseb
2013-Oct-05, 01:18 PM
How will you block neutral stuff? Dust at 0.99c will really mess up your forward windows.

Noclevername
2013-Oct-05, 01:25 PM
How will you block neutral stuff? Dust at 0.99c will really mess up your forward windows.

I was thinking laser broom or droplet spray. Also, my forward window would probably be a chunk of frozen hydrogen fuel the size of a comet head.

caveman1917
2013-Oct-05, 04:21 PM
You could also try ionizing it ahead of you. I think this option was explored somewhat in depth with regards to the Bussard ramjet approach.

Noclevername
2013-Oct-08, 10:53 AM
So, about that magnetic field strength for c-rays? Any ideas? Estimates? Guesses?

Noclevername
2013-Oct-12, 03:37 AM
Anyone? Anyone? Bueller?

lpetrich
2013-Oct-13, 03:47 AM
Rigidity (electromagnetism) (https://en.wikipedia.org/wiki/Rigidity_(electromagnetism)) is a good place to look for how much magnetic field.

Rigidity = (magnetic field) * (particle's gyroradius)
Gyroradius is radius of orbit around a magnetic-field line

Rigidity in tesla-meters: 3.3356p/q where p = momentum in GeV/c and q = electric charge as a multiple of the elementary charge

Energy factor: 1/sqrt(1 - (v/c)2)
Momentum factor: (v/c)/sqrt(1 - (v/c)2)
v = 0.5c -- 1.15, 0.58
v = 0.8c -- 1.67, 1.33
v = 0.99c --7.09, 7.02

The energy here includes rest-mass energy.

So if you use a field of 1 tesla (104 gauss), a proton coming at you at 0.99 c will have a momentum of 7 GeV/c, meaning that its gyroradius will be 23 m. One will need some awfully big magnets.

For a dust grain, one can estimate how big a crater it will dig by finding the crater's volume from (kinetic energy) / (heat of vaporization per unit volume) and finding its size as the cube root of that.

Noclevername
2013-Oct-13, 04:12 AM
Thank you!

lpetrich
2013-Oct-13, 04:55 AM
Now an interstellar dust-grain impact. A dust grain should have a density of 1 to 3 g/cm3 -- that's ice to rock.

Let's see how much energy density some shielding material would need to vaporize. I'll choose aluminum.
Atomic weight: 27
Density: 2700 kg/m^3
Melting point: 660 C, 933 K
Boiling point at 1 atm: 2519 C, 2792 K
Heat capacity at 25 C: 24.2 J/mol/K, 0.897 J/g/K
Heat of boiling: 294 kJ/mol, 10500 kJ/kg
Heat of melting is usually 1/8 to 1/4 the heat of boiling

From 0 K to boiled aluminum: 13000 J/g or 3.5 *107 J/m3

Best case for interstellar dust: 1000 kg/m3
Moving at relativistic speed (multiply by c2): 9*1019 J/m3

So a relativistic dust grain will excavate about 2.6*1012 of its volume of aluminum, or a size ratio of 14000. For a size of 0.1 microns, that's a crater size of about 1.4 mm.

Number density of interstellar dust grains: 1 per million cubic meters
So a square meter of spacecraft area should encounter 1 dust grain every 1000 km.
The forward area should be covered with dust-grain craters when it has traveled about 5*108 or 3 AU's. It will also be ablated by about 1.4 mm.

Ablation by 1 m: 3.6*1011 m or 2400 AU or 0.012 parsecs

So one will need a thick shield to survive interstellar travel at relativistic speeds.


I could have looked up penetration depths for relativistic electrons, protons, and helium nuclei, but nist.gov is likely shut down.


Souces: Wikipedia on Density (https://en.wikipedia.org/wiki/Density), Melting point (https://en.wikipedia.org/wiki/Melting_point), Boiling point (https://en.wikipedia.org/wiki/Boiling_point), Heat capacity (https://en.wikipedia.org/wiki/Heat_capacity), Enthalpy of fusion (https://en.wikipedia.org/wiki/Enthalpy_of_fusion), Enthalpy of vaporization (https://en.wikipedia.org/wiki/Enthalpy_of_vaporization)

Lecture 11: Interstellar Medium (http://www.astronomy.ohio-state.edu/~ryden/ast162_3/notes11.html) (dust number density)

Noclevername
2013-Oct-13, 08:10 AM
One will need some awfully big magnets.

Given the kind of propulsion technology needed to reach that speed (almost certainly an advanced fusion rocket or antimatter rocket) then extremely big, extremely powerful magnets will probably be an integral part of the ship design.

SkepticJ
2013-Oct-13, 07:45 PM
Would a shield have to be hard and ablate? What if it's relatively soft, and interstellar dust just shoots into it until it slows to a stop--sort of like bullets into gelatin? Thanks universe for the free matter!

Noclevername
2013-Oct-13, 08:00 PM
Would a shield have to be hard and ablate? What if it's relatively soft, and interstellar dust just shoots into it until it slows to a stop--sort of like bullets into gelatin? Thanks universe for the free matter!

At relativistic speeds, that probably wouldn't be practical, dust motes would hit like bombs no matter the texture of the target. Material shields would be blown apart or worn away quickly. A multi-layered Whipple shield might work, assisted by a laser broom or ionizing particle beam.

Anyway, the dust is not the subject I'm after, I still would like to know how to shield against cosmic rays.

lpetrich
2013-Oct-13, 08:24 PM
Would a shield have to be hard and ablate? What if it's relatively soft, and interstellar dust just shoots into it until it slows to a stop--sort of like bullets into gelatin? Thanks universe for the free matter!
The problem is the speed that the grains are traveling at relative to the spacecraft. Their kinetic energy per unit mass will be MUCH greater than the energy per mass needed to vaporize even the most refractory materials. I invite you people to try calculating that quantity for various materials.

For aluminum, I've calculated that one needs 1.3*107 joules/kg to vaporize it. It's easy to use the Newtonian kinetic-energy formula on that, and I find 5.1 km/s.

I've found Micrometeoroids and Space Debris - The Eureca Post-Flight Analysis (http://www.esa.int/esapub/bulletin/bullet80/ace80.htm) which discusses dust impacts on a spacecraft that had been retrieved from orbit. Earth-orbit dust: 10 km/s, interplanetary dust: 20 km/s. "Typically, a projectile is 2 or 3 times smaller than the pit diameter."

That's about right for my vaporization model.

SkepticJ
2013-Oct-13, 09:30 PM
Anyway, the dust is not the subject I'm after, I still would like to know how to shield against cosmic rays.

Pb

lpetrich
2013-Oct-14, 07:23 AM
Lead? Shielding against ionizing radiation is *not* a property unique to it, despite a misconception that some people seem to have. *Anything* will shield against ionizing radiation if it is thick enough, and lead is convenient because it does not have to be as thick as steel or aluminum or concrete or brick or glass or cinderblock or water or wood.

In fact, gold is even better than lead, but it's much more expensive.

Noclevername
2013-Oct-14, 07:37 AM
Actually, for charged particles a shielding material with a high hydrogen content is preferred. C-rays hitting dense metals will produce Bremsstrahlung radiation. As the mass of fuel will probably be hydrogen, that's not a major problem early on, but as those fuel tanks run dry you have less and less particle-absorbing shielding mass. Hence why I'm interested in the magnetic shield option.

SkepticJ
2013-Oct-14, 10:35 PM
Lead? Shielding against ionizing radiation is *not* a property unique to it, despite a misconception that some people seem to have. *Anything* will shield against ionizing radiation if it is thick enough, and lead is convenient because it does not have to be as thick as steel or aluminum or concrete or brick or glass or cinderblock or water or wood.

In fact, gold is even better than lead, but it's much more expensive.

It's down to density, right? Uranium 238 should be even better than gold. True, it is mildly radioactive, but with a half-life about the age of the Earth, it wouldn't hurt.

Noclevername
2013-Oct-15, 12:41 AM
It's down to density, right? Uranium 238 should be even better than gold. True, it is mildly radioactive, but with a half-life about the age of the Earth, it wouldn't hurt.

Against Gamma, maybe it wouldn't hurt. Against relativistic protons? Not so much.

eburacum45
2013-Oct-16, 03:22 AM
One kind of shield I've considered is an active shield of some sort. A stream of particles, maybe water vapour, is projected forward into the path of the ship, interacting with the interstellar medium to become a gas or plasma which expands and is pushed back towards the ship, where some or most of it is collected for reuse. Intercepting dust particles in front of the ship reduces damage to the shield, as the dust particles are converted into plasma before hitting the solid structure. Some sort of magnnetic funnel might be able to contain the gas/plasma in a night tight pillow in fron of the ship (but the magnetic field would need to be generated by some kind of loop, which would itself be vulnerable to erosion).

Noclevername
2013-Oct-16, 03:30 AM
One kind of shield I've considered is an active shield of some sort. A stream of particles, maybe water vapour, is projected forward into the path of the ship, interacting with the interstellar medium to become a gas or plasma which expands and is pushed back towards the ship, where some or most of it is collected for reuse. Intercepting dust particles in front of the ship reduces damage to the shield, as the dust particles are converted into plasma before hitting the solid structure. Some sort of magnnetic funnel might be able to contain the gas/plasma in a night tight pillow in fron of the ship (but the magnetic field would need to be generated by some kind of loop, which would itself be vulnerable to erosion).

It's sounds like a variant of a "droplet shield", the kind proposed for the Valkyrie starship (http://www.projectrho.com/public_html/rocket/slowerlight.php#id--Valkyrie_Antimatter_Starship) (scroll down a bit to find it)

eburacum45
2013-Oct-16, 04:23 AM
It's sounds like a variant of a "droplet shield", the kind proposed for the Valkyrie starship (http://www.projectrho.com/public_html/rocket/slowerlight.php#id--Valkyrie_Antimatter_Starship) (scroll down a bit to find it)

Absolutely. It is at least partly inspired by the Valkyrie, although we were discussing similar shields years ago at Orion's Arm. The ISV Venture Star uses a similar tech, with the addition of free-flying Whipple Shields.

Noclevername
2013-Oct-18, 09:13 AM
https://www.google.com/#q=relativistic+cosmic+ray+shielding

Returned 8 results, none of which I have the math skills for or else are math-free generalities, then skipped right to "similar searches"

lpetrich
2013-Oct-18, 02:45 PM
Did anyone in the Orion's Arm project try to estimate how much material would have to be sacrificed in a droplet shield? I ask that because droplets may drift away.

NIST Physical Reference Data (http://www.nist.gov/pml/data/) is now back. It has big collections of data, like NIST Stopping-Power and Range Tables: Electrons, Protons, Helium Ions (http://www.nist.gov/pml/data/star/index.cfm)

One can work out how much shielding one needs against interstellar particles. Electrons are all stopped in less than a cm, but protons can travel several meters. In graphite, a proton with its mass of kinetic energy will travel about 335.5 g/cm^2. With a density of 1.7 g/cm^3, that's 2 meters. In iron, its stopping distance is 420.7 g/cm^2, and at its density of 7.874 g/cm^3, that gives 53 cm. Uranium is even better, with a stopping distance of 593.0 g/cm^2 and a density of 19.1 g/cm^3, giving 31 cm. Lead isn't as good, because of its lower density, 11.34 g/cm^3, but gold is also good, with a density of 19.30 g/cm^3.

Going to 10 GeV for protons, I find: graphite: 5337. g/cm^2, 31 m, iron: 6389. g/cm^2, 8.11 m, uranium: 8456. g/cm^2, 4.42 m

That's a kinematic gamma factor of 11.7

eburacum45
2013-Oct-19, 12:48 PM
The amount of loss from a droplet shield would be reduced if it could be contained within a magnetic funnel of some sort, something like the funnel of a Bussard ramjet. Interaction with interstellar hydrogen would ionise the droplets, and if this sort of funnel is even possible, it could collect the interstellar medium as well - you might even make a profit. Collecting material from space en route is one of the dreams of interstellar spacefight- you could use it for added protection, or as propellant.

Noclevername
2013-Oct-19, 01:13 PM
The amount of loss from a droplet shield would be reduced if it could be contained within a magnetic funnel of some sort, something like the funnel of a Bussard ramjet. Interaction with interstellar hydrogen would ionise the droplets, and if this sort of funnel is even possible, it could collect the interstellar medium as well - you might even make a profit. Collecting material from space en route is one of the dreams of interstellar spacefight- you could use it for added protection, or as propellant.


Which brings us right back to the OP question about magnetic field strength! What a co-inky-dink. :D

Noclevername
2013-Nov-07, 07:19 AM
So if you use a field of 1 tesla (104 gauss), a proton coming at you at 0.99 c will have a momentum of 7 GeV/c, meaning that its gyroradius will be 23 m. One will need some awfully big magnets.


I could have looked up penetration depths for relativistic electrons, protons, and helium nuclei, but nist.gov is likely shut down.


Bumpity bump bump bump!

So, now does anyone know how to find values for the other C-ray particles vs magnets? I have given it my usual pathetic try (including nist.gov) but my research (and math) skills are weak.