*Our recent discussion of deep space magsails propelled by neutral particle beams inspired a lot of comments and a round of comment response from author Jim Benford. For those just joining us, Benford had studied a magsail concept developed by Alan Mole and discussed by Dana Andrews, with findings that questioned whether interstellar applications were possible, though in-system work appeared to be. The key issue was the divergence of the beam, sharply reducing its effectiveness at the sail. Today we’ll wrap up the particle beam sail story for now, with Jim’s thoughts on the latest round of comments. The full paper on this work is headed for one of the journals for peer review there and eventual publication. I’ll be revisiting particle beam propulsion this fall, and of course the comments on the current articles remain open.*

**by James Benford**

Eric Hughes wrote in the comments that my work had shown only that one method of neutralizing the neutral particle beam would produce divergence. Specifically, his comment read: “I think it’s important to recall that Benford’s article last Friday only addresses one class of methods for making a neutral particle beam. He acknowledges that himself in the last sentence of the article, when he speaks of “much more advanced beam divergence technology than we have today.”

Are there other methods of producing these beams that don’t produce divergence? Let me re-state my basic argument:

- Accelerating low-energy particles in electromagnetic fields produces high-energy particle beams.
- For those electromagnetic fields to interact with the particles, the particles must be charged. Only charged particles interact with electromagnetic fields.
- Therefore, accelerating charged particles to high-energy to produce the final beam, which is then neutralized, produces neutral beams.
- I showed that the neutralization process itself would produce an irreducible divergence. This applies to all methods for producing neutral beams.
- The only possible exception would be to produce high-energy neutral particles by nuclear reactions. But nuclear reactions are not highly directional and won’t produce a narrowly collimated beam.
- Consequently, the argument I made is quite general and fundamentally limits the properties of neutral beams.

On the other comments, these remarks: James Essig is certainly correct that the Sun provides plenty enough power for thrusters to maintain the Beamer in place. A more demanding problem is how to operate such powerful thrusters while not disturbing the microradian pointing of the beam. The beam has to stay on the sail for a long time and variations in the thrusters’ sideways motion could easily direct it away from the sail.

Electrostatic and magnetic forces never cancel no matter how relativistic the beam is; certainly they are far from cancellation for the example, where gamma is only 1.02.

Eniac hopes that gravity will provide a restoring force to the momentum of the beam generator. No such thing happens. Gravity is an attractive force. There will be a restoring force only in a potential well such as a Lagrange point, but these are noticeably weak and not up to the scale of these forces.

Eniac also writes: “Would the beam be dense enough to tear the field right off the loop and carry it away, leaving the craft behind? Yes, I think moving plasma does wreak havoc on fields that way.”

But the answer is no. The magnetic field won’t depart unless the current leaves the conductor. What does it flow in then?

The transform of the magnetic field to the moving frame of the beam is given by the product of gamma, beta and the field strength. My estimate is that ionization will be easy. Eniac’s 10 GV/m for ionization, when only 13 eV is needed, would mean that there would never be ionization in the universe, so this number is ridiculously far off.

Michael and others seem to think that the charged particles will not interact strongly if they are far apart. But they cannot be far apart and part of a beam going out to hit this 270 m sail. Divergence inevitably follows.

Comments on this entry are closed.

Regarding

On the other comments, these remarks: James Essig is certainly correct that the Sun provides plenty enough power for thrusters to maintain the Beamer in place. A more demanding problem is how to operate such powerful thrusters while not disturbing the microradian pointing of the beam. The beam has to stay on the sail for a long time and variations in the thrusters’ sideways motion could easily direct it away from the sail.

Well, who says the problem cannot be addressed and solved. We are talking about degrees of stability here.

Perhaps the beam will have some jitter after all but can be engineered to become suitably stable.

The thrusters side way motion could easily redirect the beam.

The thrusters may have several included power levels including one for fine course adjustments.

Additionally, the thruster could be housed in a magnetic coupling or other electrodynamic bearing to isolate the beamer from the jitter or perhaps the beamer can include a superconducting housing which would be suspended in place by the Meissner effect.

A spring based suspension mechanism may also work.

Yes, magnetic and electric fields can cancel in terms of their effects on material objects. One simply need only deploy the magnetic and electric fields so that the net flux density as felt by an object is reduced to zero. An object can be both electrically and magnetically charged at the same time.

In fact non-magnetic materials in many cases can be polarized by suitably strong magnetic fields and thus be fully or partially suspended. It therefore is no conceptual stretch to assume sufficiently strong magnetic fields can be used to balance the g-forces experienced by crew members of rapidly accelerating spacecraft.

Electrostatic and magnetic forces never cancel no matter how relativistic the beam is; certainly they are far from cancellation for the example, where gamma is only 1.02.

Well, if the beam includes a mixture of positive and negative charges, the net effect on the beam is no inter-particle and intra-beam electric field at all in the classical and continuous limit.

Correction, If the beam includes a mixture of an equal number of positive and negative charge units, the net effect on the beam is no inter-particle and intra-beam electric field at all in the classical and continuous limit.

[Editor’s Note: I don’t usually post the same comment in two different places, but Alan Mole’s discussion, submitted to an earlier thread on particle beam propulsion and magsails, is obviously relevant here as well, given that Jim Benford’s analysis was put together because of it.]

Thanks to everyone who has commented.

I wrote the original paper that was discussed here April 3. Comments seemed to have petered out and I moved on. Recently discussion has started again, so I’ll try to catch up.

Many comments show confusion over what I proposed or discuss issues already addressed in the paper, so I will be happy to send you a copy if you write: RAMOLE@AOL.COM.

Geoffrey Landis has suggested that using a plasma of mercury would solve the dispersion problem because millions of atoms would condense into tiny droplets. The atoms have random lateral speeds and directions but these would cancel each other when they were grouped together so beam divergence would be very low. Jim Benford objects:

“Geoff Landis’ proposal to reduce beam divergence, by having neutral atoms in the particle beam condense, is unlikely to succeed. Just because the transverse energy in the relativistic beam is only one millionth of the axial energy does not mean that it is cool. Doing the numbers, one finds that the characteristic temperature is very high, so that condensation won’t occur. The concepts described are far from cool beams. “

I am not a beam analyst but my figures show a low equivalent temperature that should allow condensation.

First, the axial velocity is high but all the atoms go at the same axial velocity so this does not count. Only their velocity relative to each other matters as to whether they adhere and form droplets. This is indeed related to their transverse velocity.

The beam goes .2 C and diverges at 3.5x10E-6 rad, so the transverse velocity is just .2 X 3 X 10E 8 m/second X 3.5 X 10 E-6 = 210m/s . (This is for hydrogen and heavier elements diverge less, so this is conservative as to temperature. That is, mercury will have a lower transverse velocity and equivalent temperature than I calculate.)

Temperature is related to speed through the ideal gas law, or

T = V^2 * M/(3 * R)

where T is degrees K, V is average velocity,m/s, in all three directions, M is the kilogram mass of a mole of the gas (201 for hg), and R is the universal gas constant or 8.31* 10^3 for Kg moles.

Then T= 210^2 * 201/(3*8.31*10^3) = 355K = 82C

Mercury should form droplets at this temperature. Thus Landis’ idea of using mercury seems promising.

This is overconservative, because V should be the average speed in X, Y, and Z directions, and 210 m/s is only in one one direction, radial out of the beam. The two perpendicular velocities are zero. I believe the actual correct number should be 210 / sqr 3 = 121 m/s, and even less because a heavier beam diverges at a smaller angle.

Again, all the droplets are going .2 c axially relative to the ground and this would be a very high temperature (and a huge energy if they impacted a still particle, and only vapor or plasma would result.) But then again, relative to matter falling into a black hole at nearly the speed of light, we are all going .99c, but that doesn’t cause us to vaporize! Relative to each other, we’re cool. (At least those of us on this list…)

Regarding the idea of a beam of protons and a parallel beam of electrons (or one intersecting at a small angle) Jim Benford also writes:

“One method of getting a neutral particle beam might be to generate separate ion and electron beams and combine them. But two nearby charged beams would need to be propagated on magnetic field lines or they would simply explode due to the electrostatic force. If they are propagating parallel to each other along magnetic field lines, they will interact through their currents as well as their charges. The two beams will experience a JxB force, which causes them to spiral about each other. This produces substantial transverse motion before they merge. This example shows why the intense fields of particle beams create beam divergence no matter how carefully one can design them.”

I have asked him if both particle streams have the same axial velocity, i.e zero axial velocity relative to each other, whether they then feel a magnetic field from the other? Or is B just zero? Again, their velocity relative to the ground seems irrelevant; relative to each other they are still. I have received no answer and I’m not a beam expert so I simply do not know.

Galacsi writes: “The launch system as envisioned by Dana Andrews and Alan Mole would be affixed to an asteroid that would provide sufficient mass to prevent the reaction from the launch of the beam from altering the orbit of the Beamer and changing the direction of the beam itself. No quantitative valuation of this has been provided to date.’ Others question what it would take to stabilize the generator in earth orbit.

Actually I (Mole) wanted the beam generator on the ground or in earth orbit. If it is in orbit we must indeed counteract its thrust but that is not hard.

If one does not want to go at lightspeed one is better off using as much ejecta mass as possible, to get the most momentum for a given energy. That’s why jets use ever-higher bypass ratios.

The beam genertor accelerates a 1 kg (2.2 lb) mass at 1000 g for 50 minutes. That’s 2200 lbs force x 50 minutes = 110,000 lb minutes. A typical rocket – say, Falcon 1 – weighs 85,000 lbs and produces 102,000 lbs force (thrust) for 2.8 minutes, or 285,000 lb minutes. This is about three times what we need, so we could get by with 28,000 lb of rocket pushing the generator and counteracting its thrust. At $200/ lb to LEO (Musk’s goal for reuseable rockets) that comes to $5.6 million, which is trivial compared to the $17 Billion I estimated for this project. This part is easy.

“August 28, 2014 at 16:16

How do we envisage keeping the superconducting wire cold? Does it need to be kept shaded and a radiator provided? Is aAlex Tolley passive system sufficient, or do we meed active cooling? “

Actually I wrote an entire appendix in the paper to show passive methods could keep it cold enough. I found that using a rectangular cross section, with the narrow side facing the sun and reflective and the wide sides facing space and black (emissive), would keep it more than cold enough.

“Appendix A Thermal Design for Temperature of 93 °K at 1 AU

Andrews and Zubrin[15] selected YBa2Cu3O7 as a superconductor with good electrical and mechanical properties for use in a magsail in the inner solar system. Its critical temperature (Tc) is 93 K. It is shown below that this temperature can be achieved at 1 AU by appropriate geometry and thermal coatings without recourse to external cooling.

Consider a 1 cm length of ribbon cable 0.2 cm by 5 cm. The size is selected for convenience in calculation; the actual sail cross section would be much smaller but have the same proportions. The sail is painted black so emissivity is 0.95, except for the sunward face which is coated with silverized teflon with an absorptance of 0.09. The solar constant is 0.136 W/cm2 so the energy absorbed on the front face is:

.09 x .2 cm x 1 cm x .136 W/cm2 = .0024 W.

Neglecting the front and rear faces, the area of the top and bottom radiating faces is 10 cm2. The resulting temperature is

T = (Energy/(emissivity x Area x Stefan-Boltzmann Constant)1/4

T= (.0024 W/( .95 x 10 cm2 x 5.67 x 10-12 J s-1 cm-2 °K-4))1/4 = 81 °K

This is well below the required Tc of 93 °K. The temperature can be lowered further by making the cable even thinner to decrease the frontal area or by coating the front with a dielectric mirror with an absorptance of less than .01 instead of the .09 used above.* Thus a magsail of YBa2Cu3O7 can be made cold enough to operate at 1 AU. It is not necessary to go to the asteroid belt; the sail can be launched from space near Earth.

* (I was wrong about dielectric mirrors, which reflect only a narrow band of wavelengths. But silver has a reflectivity of 95-99%, or absorptance of 5-1%, almost 2-10 times better than the .09 I used in the calculations.)

Alan Mole

Galacsi writes: “The launch system as envisioned by Dana Andrews and Alan Mole would be affixed to an asteroid that would provide sufficient mass to prevent the reaction from the launch of the beam from altering the orbit of the Beamer and changing the direction of the beam itself.

Well I did not write this , but it is an answer to something I wrote.

I am not sure the calculations above are very realistic , in my book to accelerate 1 kg at 1000 G (i.e 10,000/s2) , you need a force or 22,000 lbs. And you must take into account the divergence of the beam , an unknown factor , and the yield of the impact of the useful particle on the sail , an other unknown factor. So . . .

I don’t see why people are so afraid of solar electric rocket , one of these starting from the mercury orbit could attain an enormous speed before lacking of sun light.

“Only charged particles interact with electromagnetic fields.”

While this is true, the implication drawn is not. Neutral atoms composed of charged particles interact with electromagnetic fields. A trivial demonstration of this is the fact that you can see solid objects… A less trivial, that an electrostatic charge can attract a neutral bit of fluff, by inducing a dipole moment in it.

Charged particles are really, really convenient to accelerate electromagnetically, because they can be accelerated by uniform fields. However, any neutral particle which is a composite of charged particles can, in principle, be accelerated by a non-uniform field. Perhaps some work needs to be put into designing at particle accelerator on this principle?

Mind, it becomes easier to induce a dipole moment in larger particles, so an accelerator intended to accelerate neutral particles would probably work better on large molecules, better still on dust particles or droplets, and still better on macroscopic objects. In the limit, we’re discussing a mass driver, not a particle accelerator.

It may be that a neutral beam produced by such means still won’t work for propelling a star ship. But I didn’t want to leave the notion that you can’t accelerate neutral particles with electromagnetic fields unchallenged. This is unambiguously false.

It seems my comments have been very unclear, as none of it has been undeerstood. Let me try to clarify:

Gravity can be used quite easily here, using a forced orbit. If you offset a circular orbit axially, a constant axial force is needed to remain in this type of orbit. This force can perfectly provided by the recoil of a beam. No propulsion is needed. Gravitational attraction between the beamer and the body it orbits will provide the counter-force.

I phrased this wrong, depart is the wrong word. The field is screened by counteracting currents in the plasma (same as the beam). This is elementary plasma physics, and it will happen.

If you remove an electron from a nucleus, you will have to move it from 0 to 13 eV over a distance of an angstrom or so. The field strength needed to do this is enormous. I assumed only 1 eV over 1 Angstrom, which gives 10 GV/m.

The reason there is ionization in the universe is because atoms are hit by light or other particles. Static electric fields tend not to be strong enough.

“If you remove an electron from a nucleus, you will have to move it from 0 to 13 eV over a distance of an angstrom or so. The field strength needed to do this is enormous. I assumed only 1 eV over 1 Angstrom, which gives 10 GV/m.”

From the perspective of the ship, it deploys a magnetic field, which is struck by a neutral particle beam. But in the reference frame of the beam, it is a gas encountering a *moving* magnetic field, which implies an induced voltage. The voltage just has to exceed the breakdown voltage of the gas, and it will end up ionized.

Mind, there’s some question whether this would happen fast enough. OTOH, if the magnetic field holds a sufficiently dense plasma, collisions within the plasma can do the job.

My own preference might be to use a large molecule which could be triggered to ionize by UV light from the plasma contained by the magnetic field, though.

The most well-known example of a forced orbit is the

statite(http://en.wikipedia.org/wiki/Statite) invented by Robert Forward. Here, gravity perfectly counteracts the radiation force on a solar sail. Replace solar sail by beam generator and you may grasp how this is relevant here.Maybe this link will help understand what I meant by carrying (or dragging) the field away: http://www-spof.gsfc.nasa.gov/stargaze/Simfproj.htm

Excerpt:

Clearly, for the magsail we hope that the former be the case. I believe Bolonkin (http://arxiv.org/ftp/physics/papers/0701/0701060.pdf) is arguing the latter is the case and that nobody in the field has bothered to check.

Jim Benford appears to not have understood the nature of the objection at all.

Brett Bellmore

Yes, this is another way to see it, and it might help. If the gas (beam) is dense enough, breakdown requires lower fields because it works by cascading collisions between ions and atoms. Still, I do not expect a mT strength field as envisioned for the magsail to translate into the kV/m needed for breakdown, nor do I expect the beam to be dense enough to sustain breakdown. Breakdown also normally requires an anode or cathode from which charge carriers are emitted. I don’t see where those would be in this situation.

“Gravity can be used quite easily here, using a forced orbit. If you offset a circular orbit axially, a constant axial force is needed to remain in this type of orbit. This force can perfectly provided by the recoil of a beam. No propulsion is needed. Gravitational attraction between the beamer and the body it orbits will provide the counter-force.”

That is an interesting idea. I guess that would make targeting more challenging, but it would offer energy free stabilizing during beam operation. There is of course the matter of obstructing a directional beam in intevalls, or is there a workaround that is escaping me? Perhaps it would be more accurate operating the beamer on the surface of a more or less massive object in a stable location (lagrangian point) for extreme range. It will move the object, of course, but maybe its best not to stabilize during beam operation for the sake of beam accuracy. Maybe we could find an object where stabilizing is even negligible.

Gentlemen, there is a holistic view on the divergence issue of particle beams. Particle beams are clearly useful for moving things around. However, they can equally well be used as weapons. The issue is the same – beam divergence. I would assume the research on particle beam weapons, over the last half a century, has been extensive, focused, motivated, well funded and done in competition. As nothing has come up, one could assume that the divergence issue is difficult to handle.

As an afterthought to my previous post, if we did live in a ring-world of a radius equal to that of earth’s orbit, sending probes at 0.01c velocities would be really easy :-) An electromagnetic accelerator at the entire outer circumference of such a structure could comfortably accelerate things to 0.01c with the payload experiencing a very mild acceleration of about 6og. Arguable, such probes could only be send in the plane of the ring-world :-)

@James Benford

‘Electrostatic and magnetic forces never cancel no matter how relativistic the beam is; certainly they are far from cancellation for the example, where gamma is only 1.02.’

Now go to 0.99999 of c with a charged particle beam and there is a significant reduction of the repulsive force lowering divergence.

‘Michael and others seem to think that the charged particles will not interact strongly if they are far apart. But they cannot be far apart and part of a beam going out to hit this 270 m sail. Divergence inevitably follows.’

If the same amount of beam material is divided up into multiple beams a distance apart (even cm’s) then less material will need to pass through each beam. Remember the main reason why the beam diverges is because of the repulsive force of the confined charged particles i.e. there will be less ‘potential energy’ available to throw the particles apart in the first place if they are further apart. Dividing the beam up into multiple streams has a significant positive effect on the divergence as does increasing the velocity of the beam particles. Surprisingly very high velocity charged particle beams have low divergence, better than lasers, if you look at how they are made up. I and others are correct in that multiple beams have less divergence for the same power output.

I would like to see a parallel assessment of magnetic propulsion techniques versus laser type propulsion such as project ‘Dragonfly’, lets call it project ‘Ionfly’.

@Alan Mole

Care must be taken to avoid the Brewster angle though.

” There is of course the matter of obstructing a directional beam in intevalls, or is there a workaround that is escaping me? ”

The simple “workaround”, is that the axis of revolution of the orbit must point in the same direction as the beam. The recoil is along that axis, and the beam station simply orbits in a plane which is displaced from the center of the body it orbits around enough to always be experiencing net gravitational force enough to counter the recoil. Pretty easy to calculate, actually.

swage:

In the forced orbit envisioned here, the beam goes out parallel to the orbital axis, i.e. orthogonal to the orbital plane. The recoil force is compensated by shifting the orbit away from the gravitational center by a fairly small amount. There is never an occultation of the beam by the orbited body.

I think this should be the least challenging method with respect to targeting, because the beamer has no noisy propulsion system and is isolated from all sources of vibration other than its own operations.

Galacsi writes:

“I am not sure the calculations above are very realistic , in my book to accelerate 1 kg at 1000 G (i.e 10,000/s2) , you need a force or 22,000 lbs. And you must take into account the divergence of the beam , an unknown factor , and the yield of the impact of the useful particle on the sail , an other unknown factor.”

I believe my calculation is correct. One kilogram equals 2.2 lbs. To accelerate 1 lb to 1g requires one lb of force. (E.g. 1 lb weighs 1 lb and produces 1 lb of force against something holding it up. If the holder is removed the 1 lb drops at 1g. To accelerate 1 lb at 1000 g requires 1000 lbs of force. To accelerate 2.2 lbs requires 2200 lbs of force as I said, not 22,000 lbs as Galaxsi says. In the MKS system there is indeed a 10 times multiplier involved, but not in the English system. The transition to MKS will cost many mistakes!

In the paper I said I assumed 100% efficiency; Andrews said 60% I think and I assumed some improvement over 50 years. For lower efficiencies a larger beam force will indeed be required.

In case my own comments remain unclear to others: Brett Bellmore has it exactly right on using a forced orbit to provide gravitational recoil compensation.

@Eniac

Silly me. That makes perfect sense that way, of course.