We spend a lot of time talking about how to get an interstellar probe up to speed. But what happens if we do achieve a cruise speed of 12 percent of the speed of light, as envisioned by the designers who put together Project Daedalus back in the 1970s? Daedalus called for a 3.8-year period of acceleration that would set up a 46-year cruise to its target, Barnard’s Star, some 5.9 light years away. That’s stretching mission duration out to the active career span of a researcher, but it’s a span we might accept if we could be sure we’d get good science out of it.
Maximizing the Science Return
But can we? Let’s assume we’re approaching a solar system at 12 percent of c and out there orbiting the target star is a terrestrial planet, just the sort of thing we’re hoping to find. Assume for the sake of argument that the probe crosses the path of this object at approximately ninety degrees to its orbital motion trajectory. As Kelvin Long shows in a recent post on the Project Icarus blog, the encounter time, during which serious observations could be made, is less than one second. A Jupiter-class world, much larger and observable from a greater distance, itself offers up something less than ten seconds at best for scientific scrutiny.
That’s a paltry return on decades of construction and flight time, not to mention the probable trillion or more dollars it would take to build such a probe, and it hardly compares well to what we’ll be able to achieve with even ground-based telescopes as the next generation of optics becomes available. What to do? Long is looking into these issues as part of the Project Icarus team, which is revisiting the Daedalus concept to see how changing technologies could alter the flight profile and produce a mission whose results would be substantially more useful.
Image: The Daedalus starship arrives in the Barnard’s Star system. Credit and copyright: Adrian Mann.
One option is to do the unthinkable. Instead of ramping up flight speed to get to the destination more quickly, perhaps a better alternative is to slow the mission down. There are two ways to do this: 1) Aim for a slower cruise speed in the first place and/or 2) attempt to decelerate the vehicle. The latter choice is a genuine conundrum for reasons Long makes clear:
Another option being examined [for deceleration] is reverse engine thrust, but the problem with this is that if we assume an equal acceleration-deceleration profile then the mass ratio scales as squared compared to a flyby mission and so requires an enormous amount of propellant; definitely a turn-off for a design team seeking efficient solutions.
What this boils down to is that if you want to carry enough propellant to turn your spacecraft around and decelerate, you have to carry that additional propellant with you from the start of the mission. The rocket equation yields a stubborn result — the requirement for propellant increases not proportionally but exponentially in relation to the final velocity required. The initial fuel mass becomes vast beyond comprehension when we apply the numbers to slowing an interstellar craft, which is why the Icarus team, as it looks into deceleration, is examining ideas like magsails, where the incoming vehicle can brake against the star’s stellar wind.
A magsail or, for that matter, various other sail possibilities (Robert Forward described decelerating a manned interstellar vehicle by lightsail in his novel Rocheworld) offers the unique advantage of leaving the fuel out of the spacecraft — you’re braking against a stellar particle flux, or against starlight itself. But whether or not such ideas prove feasible, they’re more likely to at least help if the spacecraft is traveling slower to begin with, making it easier to decelerate further. A slower transit also reduces stress on the vehicle’s engines and structure during the boost phase.
The Case Against Going Faster
Long notes that Project Icarus is far from having answers on just what cruise speed will be optimal — Icarus is a work in progress. But these issues are at the heart of the interstellar quest:
…all of this analysis goes to the heart of whether a flyby probe such as Daedalus is really useful given what it took to get there. The potential science return is massively amplified by performing a deceleration of the vehicle and although it is a significant engineering challenge this is why the Icarus team decided to address this problem; and it is a problem, even if you choose to just decelerate sub-probes. Coming up with a viable solution to the deceleration problem in itself would justify Project Icarus and the five years it took to complete the design process.
Supposing you gave up on trying to stop the probe in the destination system, but simply made your goal to slow it down enough to make protracted scientific observations as it passed through? It’s clearly an option, and again we’re considering a trade-off between the shortest travel time and the ability to maximize science return. Interstellar flight is a challenge so daunting that it makes us question all our assumptions, not the least of which has always been that faster is better. Not necessarily so, the Icarus team now speculates, and perhaps a fusion/magsail hybrid vehicle will emerge, a significant upgrade from the Daedalus design. And this reminds me of something I wrote about magsails back in 2004 in my Centauri Dreams book:
At destination, a magnetic sail is our best way to slow [the] probe down, with perhaps a separate solar sail deployment at the end that can brake the vessel into Centauri orbit. If you had to bet on the thing — if the human race decided a fast probe had to be launched and was willing to commit the resources to do so within the century — this is where the near-term technology exists to make it happen.
Of course, I now look back on that passage and shudder at my use of the phrase ‘near-term’ to describe the vehicle in question, but maybe a very loose definition of ‘near-term’ to mean ‘within the next few centuries’ will suffice (hey, I’m an optimist). In any case, when we’re talking journeys of forty trillion kilometers (the distance to the nearest stellar system) and more, a century or two seems little enough to ask. And while I do believe this, I rejoice at the spirit of Project Icarus, whose team presses on to discover whether such a thing could be attempted in an even shorter time-frame.
As said, 6,428,571 m/s^2 acceleration was achieved in 1987 in a rail-gun for a 0,7g projectile. Apparently, even better accelerations were achieved:
“In 1987 a successor was created, project EDO-1, that used projectile with a mass of 0.7 g and achieved speeds of 3,000 m/s, and with a mass of 1.1 g reached speeds of 2,400 m/s. It used a track length of 0.7 m. According to those working on it, with other modifications it was able to achieve a speed of 4,500 m/s. The aim was to achieve projectile speed of 7,000 m/s. At the time, it was considered a military secret.”
If we assume that, in a straight accelerator located in empty space (a position with significant advantages over an earth based one for building large tructures, for having vacuum, for no gravity, etc), an acceleration of 9,000,000m/s^2 can be achieved ‘contact free and continuously’ (a conservative enough estimate), then, in order to reach 0.1c, the accelerator wold have to be 50,000km long (as per L=1/2 v^2/a).
Hardly unachievable – either structurally and economically.
The probem becomes not ‘is the accelerator feasible?’ but ‘is the accelerator easier to design and build/cheaper than a high-power laser for accelerating fuel pellets or viceversa?
Returning to issue of Icarus, another advantage of having that probe stop at the Alpha Centauri system is that by holding a relatively small amount of fuel in reserve, once it had surveyed that system, the probe could spend a few years traveling to the 0.21 LY distant Proxima Centauri.
Andrew W
About Icarus:
A starship very similar to Icarus could be used in my proposed mission architecture.
It’s just that its fuel tanks will be empty during acceleration. They will be filled with fuel after Icarus reaches 0.1c, fuel that will be used for deceleration.
The main difference is that Icarus doesn’t have a Bussard ramscoop, while my starship has.
As it turns out, the Bussard ramscoop may not be necessary after all (or it can be very small – a few tens of meters) – in the sailbeam propoal, the microlenses are actively guided to a target only a few mwter wide on the ship.
A 0.7 meter railgun is quite different from a 50,000 km long accelerator. Apples and oranges.
Contact free and continuously AND at high velocity. For starters, calculate the maximum acceleration that can be achieved statically by taking the worlds strongest permanent magnet and holding it near the worlds strongest superconducting electromagnet. I bet you’ll come up a good number of orders of magnitude short. Then consider how fast you would have to reverse the field in that electromagnet as the projectile whizzes by at 0.1c. “Conservative enough” is a true howler.
This would have to be weighed against spending those same few years further exploring Alpha. Of course, if there are no planets there, we will go to some other system, instead, anyway.
You are looking for a deuteride. Lithium deuteride is a wonderful fuel, because it is solid. It will be of great value for a Daedalus/Icarus style ship, because you can forget about tanks and their mass. It is more problematic to burn efficiently (most likely by breeding the lithium into tritium and He3), but worth some trouble because of the above, and because it is cheaper than He3. Much cheaper.
It won’t be much good for your pellets, though, because the deuterium will outgas at 600K, and because of all the other issues. At least you are now gradually approaching the Kare proposal, which is substantial progress.
About the fuel pellets’ composition:
Lithium deuteride, in vacuum melts at 680°-697°C, with virtually no decomposition.
680-697C is FAR above 600k.
As I said – heat by friction with the interstellar medium at 0.1c is a problem solvable today.
About the accelerator:
““Conservative enough” is a true howler.”
I disagree.
6,428,571 m/s^2 is NOT the highest acceleration achieved in rail-guns:
“in October 2006, the U.S. Navy has tested a railgun that accelerates a 3.2 kg (7 pound) projectile to 2.4 kilometers per second (7,875 feet per second).”
“On January 31, 2008 the US Navy tested a railgun that fired a shell at 10.64 MJ with a muzzle velocity of 2,520 m/s.[16] Its expected performance is a muzzle velocity over 5,800 m/s, accurate enough to hit a 5 meter target over 200 nautical miles (370.4 km) away while firing at 10 shots per minute.”
The most recent test: http://www.wired.com/dangerroom/2010/12/video-navys-mach-8-railgun-obliterates-record/
The US Navy already achieved accelerations greater than 9,000,000m/s^2.
Plus, consider:
– the US Navy railgun’s electromagnets/other components are of small size – a problem you won’t have with a space-based accelerator – which translates into higher acceleratioins (and other advantages);
-the projectiles launched weigh kilograms; the fuel pellets would only weigh a few grams – which translates into higher accelerations (and other advantages);
-your power would be given by fusion reactors.
9,000,000m/s^2 and 50,000km IS conservative.
The problems you mentioned are solvable – the physical laws more than allow that – without resorting to planet-scale engineering.
Now let’s look at the sailbeam and its super-laser.
What are the best lasers we have today? What’s the difference in power between them and the super-laser?
Is there even a hint that such super-lasers are feasible in practice (as in, the technical problems can actually be solved without making them planet-sized – which comes with its own set of problems)? What are the technical advances needed?
My accelerator is far closer to our technological level than such a super-laser.
Give the magnitude of the challenge of interstellar flight, I don’t think accelerators of 100,000 kms length is outlandish, Eniac’s link states: “For all practical purposes, mass drivers have no velocity limit and no length limit. Acceleration has been limited thus far by the current and voltage capacity of the SCRs used for switching. Using shelf components, Mass Driver Two should achieve 500 to 1,000 g. If the SCR limitation is removed, by using ignitrons, spark gaps, or direct contact switching, performance will be limited by mechanical and thermal failure of the drive coils. Some preliminary calculations based on a four inch caliber mass driver using aluminum bucket coils and copper drive coils suggest an acceleration limit between 100,000 and 250,000 g.”
That’s 100,000 – 250,000 with aluminium buckets and copper drive coils?!
So in some respects the sail beam /micro sail concept probably has just as great or even greater uncertainties about its practicalities.
ProtoAvatar, I still don’t see a need to launch fuel pellets across interstellar distances, why launch the probe unfueled rather than fueled, when with both options the same mass has to be accelerated to the same speed over similar time periods?
I can appreciate that subatomic particles can be accelerated far more rapidly than objects of a gram or so, but why is it that it’s practical to push subatomic particles up to speeds approaching c, but that supposedly this can’t be done for large objects because the switching mechanisms would be too slow?
Andrew W
“ProtoAvatar, I still don’t see a need to launch fuel pellets across interstellar distances, why launch the probe unfueled rather than fueled, when with both options the same mass has to be accelerated to the same speed over similar time periods?”
I propose launching fuel pellets with a particle accelerator BECAUSE less fuel/mass will have to be accelerated:
Let’s look only at the acceleration phase:
A ship with ~empty fuel tanks throughout the journey (far lighter) would need far less fuel to be accelerated to 0.1c than a ship that starts with full fuel tanks (far heavier – the rocket equation is obeyed).
This means that you would have to accelerate far less fuel in the former case (accelerating fuel pellets by accelerator) than you would in the latter case (carrying the fuel on-board).
Now let’s look at acceleration+deceleration:
By using a fuel pellets accelerator, you will have to accelerate:
-first, the fuel pellets that a ship carrying the fuel on-board would need to decelerate from 0.1c to 0c; the quantity of this fuel obeys the rocket equation.
These fuel pellets will be accelerated to just below 0.1c; after it reached 0.1c, the starship will fill its fuel tanks with this fuel, for deceleration.
-second, the fuel pellets needed to accelerate a ship with ~EMPTY FUEL TANKS throughout the journey from 0 to 0.1c (this is less – BY FAR – than the quantity of fuel needed to accelerate a ship that starts with full fuel tanks to 0.1c – which obeys the rocket equation).
These fuel pellets will be accelerated with a speed that decreases from near 0.1c to almost 0; they will be collected by the starship during its acceleration phase.
By carrying the fuel on-board (rocket equation):
You would STILL need to accelerate to 0.1c the fuel needed for deceleration.
If you send fuel pellets by accelerator, you also need to accelerate an equal quantity of fuel to 0.1c (no advantage/disadvantage here).
AND you would need to accelerate a ship FILLED WITH THIS MUCH FUEL (the fuel needed for deceleration) to 0.1c. The rocket equation dictates that the fuel needed increases exponentially with delta V; this becomes an enormous amount of fuel (FAR more – by orders of magnitude – than in my ‘pellets by accelerator’ proposition); indeed, it’s an impractically large quantity of fuel.
But, if you send fuel pellets by accelerator, the amount of fuel you must send for acceleration is actually smaller than the amount of fuel you sent previously for deceleration (a gigantic advantage for my proposition); if it’s feasible for you to accelerate the ship to 0.1c, with my mission architecture it becomes feasible to accelerate/decelerate the ship from 0c-0.1c-0c (you will NOT even double your cost/amount of fuel sent).
@ProtoAvatar
We will just have to continue to disagree on this one. Not that I think the super-laser is particularly doable, mind you.
It is because of the large charge/mass ratio of particles. Large objects have comparably minuscule charge/mass ratios, even if charged to extreme voltages. Thus they cannot be accelerated nearly as effectively.
Copper for stationary coils and aluminum for the moving coil is the very best you can do, because what matters is conductivity for the one and specific conductivity for the other. Note also that the 250,000 here is a lot less than what the secret military railgun can (purportedly) do. Railguns work much differently from coil guns, anyway, and like chemical cannons, they cannot be scaled to higher energies.
Superconductors would be the obvious next step, but they are no silver bullet, due to other issues (see below).
What they do not mention is that there is, in fact, a limit: as the velocity of the projectile increases, coil depolarization has to be faster and faster. This leads to a “suck-back” effect that limits the achievable muzzle energy. The electromotive force in a coil trying to accelerate a 0.1c projectile would be astronomical and vaporize the coil instantly. This is why we have no practical way yet to accelerate projectiles to orbit, much less any faster. Many of the issues are discussed in this excellent paper:
http://www.math.temple.edu/~wds/homepage/launcher.abs
http://www.math.temple.edu/~wds/homepage/launcher.ps
The fact is, at the moment people are striving pretty hard to achieve something close to orbital velocity, which is laughably trivial compared with what we have been talking about.
Here is the nextbigfuture article about the issue, if you want to do some more reality checking:
http://nextbigfuture.com/2008/02/magnetic-catapult-feasible-advanced.html
Note: Maximum acceleration 19,500 m/s^2 for that featured UTSTAR module. I am beginning to wonder if maybe the fantastic railgun acceleration claimed for that top secret military project of a small Eastern European country might not be quite as well documented as we had assumed.
Eniac
About magnetic field strength:
http://en.wikipedia.org/wiki/Orders_of_magnitude_%28magnetic_field%29
“45T strongest continuous magnetic field yet produced in a laboratory”
“88.9 T strongest (pulsed) magnetic field yet obtained non-destructively in a laboratory”
The two values differ by a factor of ~2 (not by orders of magnitude).
And both are generated by large electromagnets – meaning the rail-guns’ electromagnets’ field strength is substantially below 88.9T.
About the mass driver:
http://en.wikipedia.org/wiki/Mass_driver
“A 1 km long mass driver made of superconducting coils can accelerate a 20 kg vehicle to 10.5 km/s at a conversion efficiency of 80%, and average acceleration of 5,600 g”
20 kg, in 1 km, reach 10.5km/s?
I want to launch fuel pellets weighing 1 gram (20000 thousand times lighter!), through a considerably longer mass driver.
Here’s a calculator:
http://xeriar.com/calculators/relativistic_kill_vehicles_mass_driver
ProtoAvatar, I still don’t get your reasoning.
I’m not advocating burning the fuel on the ship during the acceleration phase, all the fuel on the ship at the time it’s launched remains unused until it’s needed for the deceleration, so in both cases the rocket equation doesn’t apply during acceleration.
In both cases both the ship and the fuel for deceleration need to be propelled to about 0.1c, this can either be done to the two separately, or together. But in both cases if the ship has a mass of 50,000 tonnes prior to the start of deceleration, 50,000 tonnes needs to be accelerated to 0.1c.
Eniac: “It is because of the large charge/mass ratio of particles. Large objects have comparably minuscule charge/mass ratios, even if charged to extreme voltages. Thus they cannot be accelerated nearly as effectively.”
That doesn’t address the point I’m making, I acknowledge in the paragraph you quote that the rate of acceleration for large objects will be very low compared to subatomic particles. My question is why don’t your objections like “suck-back” and coil depolarization speeds stop the LHC from pushing subatomic particles to 0.999c or there abouts?
Because the charge/mass ratio allows us to use electrostatic fields for acceleration, which does not have these problems.
I am not sure what you are trying to say. Perhaps you have misinterpreted the meaning of “continuous acceleration” to mean “continuous magnetic field”. The problem is not to have a strong static magnetic field, it is just the opposite: the field must change while the projectile passes, and it must do it everywhere along the accelerator, at just the right time, to affect continuous acceleration. One problem with this is that the faster the projectile moves, the faster the field must change, the larger the electromotive force (EMF). The EMF is limited by breakdown voltage and other hard limits dictated by available materials, and there is no room for 4 orders of magnitude in improvement, not even in theory.
Again, I am not sure what you are trying to say here. The mass driver you mention is hypothetical, but not beyond possible future technology. Yours, on the other hand, must achieve 0.1c, which is 3,000 times faster. It would have to be 9,000,000 km long (30 times the distance to the moon), perfectly straight and still, and be able to impart that constant acceleration of 5,600 g on the projectile along the entire length, while it is zipping along at near light speed, for the most part. I am sorry, but this is so implausible on so many levels that “impossible” is appropriate here, if it ever is.
I cede my prize for the understatement of the year to your ingenious use of the words “considerably longer”.
Andrew W
Yes, the same amount of fuel needed for deceleration (50.000 tonnes) must be accelerated to 0.1c.
The accelerator will consume fuel in its reactor in order to accelerate these 50.000t of fuel to 0.1c – ONLY these 50.000t, not a gram more will be accelerated.
If you want to accelerate, let’s say, 100.000t to 0.1c, you will only have to burn twice as much fuel in the accelerator’s fusion reactor (the needed amount of fuel increases LINEARLY) – because you only accelerate 100.000t to 0.1c.
The ship must consume fuel from its fuel tanks.
But according to the rocket equation, at first, it will have to accelerate 50.000t+the fuel it will need to carry these 50.000t the rest of the way to 0.1c (which is a LOT) – this suplemental weight to be accelerated means that, initially, a ship with on-board fuel will need to consume a LOT more fuel than an accelerator’s reactor (which doesn’t need to accelerate more than 50.000t).
This will continue throughout the acceleration because, at any moment, the ship will have to accelerate the 50.000t+the decreasing, but still substantial amount of fuel it will need to accelerate these 50.000t further.
And, if you want to accelerate 100.000t to 0.1c with on-board fuel, the amount of fuel needed will increase EXPONENTIALLY, NOT linearly – because, initially, you have to carry the fuel which will carry the fuel which will carry the fuel which will carry……these 100.000t to 0.1c.
Eniac
“I am beginning to wonder if maybe the fantastic railgun acceleration claimed for that top secret military project of a small Eastern European country might not be quite as well documented as we had assumed.”
As I already mentioined, the US Navy tested rail-guns which accelerated projectiles weighing kilograms(!) to comparable velocities.
Unless these are, too, staged, in a massive disinformation campaign, that yugoslavian rail-gun performances are accurate.
ProtoAvatar, I think perhaps you’re not reading what I’m actually saying, perhaps a few modifications to my 19:52 comment:
I’m not advocating burning the fuel on the ship during the acceleration phase, all the fuel on the ship at the time it’s launched remains unused until it’s needed for the deceleration, so in both cases the rocket equation doesn’t apply during acceleration.
In both cases both the ship and the fuel for deceleration need to be propelled to about 0.1c, by the launcher, this can either be done to the fuel for deceleration and the ship separately (first the launcher accelerates the fuel in the form of pellets, then the unfueled ship, or together, with the fuel for deceleration already on the ship, the launcher, through the kinetic pellets (not fusion pellets) again accelerating both. IN BOTH CASES THE SHIP DOES NOT USE ITS FUSION ENGINES DURING THE ACCELERATION PHASE.
Eniac, I first came across railguns in a popular science article around 1980, it was a 1 metre gun at white sands that was firing a 1 gram projectile at 7 – 10 km/sec. I’ve tried googling for it but have only found references to a light gas gun at about that time, the article though had a diagram of the rail gun and the diagram was a rail gun so I don’t think I can be confusing the two.
“I am sorry, but this is so implausible on so many levels that “impossible” is appropriate here, if it ever is. ”
My God Man! Do I have to start quoting Clarke’s laws to you?! :-)
“The problem is not to have a strong static magnetic field, it is just the opposite: the field must change while the projectile passes, and it must do it everywhere along the accelerator, at just the right time, to affect continuous acceleration. One problem with this is that the faster the projectile moves, the faster the field must change, the larger the electromotive force (EMF). ”
Particles accelerators (the strongest – LHC) accelerate elementary particles to near light-speed.
The betatron uses a changing magnetic field to accelerate particles to near light speed (far above 0.1c) – it changes the magnetic field at just the right time, everywhere along the accelerator (yes, for the betatron the problem was solved 70+ years ago).
I even found how it does this:
“For the production of the rapidly changing magnetic ?eld, with the
proper dependence on the radius, ?nely laminated iron pole faces were made from 0.003-inch silicon steel sheets. The return magnetic circuit made from the same material was interleaved for mechanical strength; and the roughly circular central pole pieces were formed by stacking with di?erent widths of laminations as shown in Fig. 2. Each pole piece was capped by a disk of radially arranged laminations so that perfect circular symmetry was achieved at the pole surfaces (B, Fig. 2). The whole pole face was held together by a thick Transite or asbestos board ring about its perimeter, with cement of water glass and ?int dust ?lling the cracks between the laminations and hardened by baking. The pole caps were held against the pole pieces by eccentric wedges between the Transite rings.”
from Kerst, D. W. “The Acceleration of Electrons by Magnetic Induction.”
Most particle accelerators use electrostatic fields (RF cavities) to do that – again they have no problem changing their fields.
In any case, the theoretical limit for changing electromagnetic fields is the speed of light – meaning this is in no way a fundamental problem.
“”About the mass driver:
http://en.wikipedia.org/wiki/Mass_driver
“A 1 km long mass driver made of superconducting coils can accelerate a 20 kg vehicle to 10.5 km/s at a conversion efficiency of 80%, and average acceleration of 5,600 g”
20 kg, in 1 km, reach 10.5km/s?
I want to launch fuel pellets weighing 1 gram (20000 thousand times lighter!), through a considerably longer mass driver. ”
Again, I am not sure what you are trying to say here. The mass driver you mention is hypothetical, but not beyond possible future technology. Yours, on the other hand, must achieve 0.1c, which is 3,000 times faster.”
Yes, my accelerator will have to achieve 0.1c (3,000 times faster) but my accelerator will have to accelerate ONLY 1g, NOT 20kg.
1g is 20,000 times lighter than 20kg.
20,000g can be accelerated to 10.5km/s in an 1km long mass driver.
1g can be accelerated how much faster during this 1 km long mass driver?
What if we make the mass driver 1,000km long?
Andrew W
“In both cases both the ship and the fuel for deceleration need to be propelled to about 0.1c, by the launcher, this can either be done to the fuel for deceleration and the ship separately (first the launcher accelerates the fuel in the form of pellets, then the unfueled ship, or together, with the fuel for deceleration already on the ship, the launcher, through the kinetic pellets (not fusion pellets) again accelerating both. IN BOTH CASES THE SHIP DOES NOT USE ITS FUSION ENGINES DURING THE ACCELERATION PHASE.”
Andrew W, in my proposition the accelerator will NOT launch the ship at all.
The accelerator will ONLY launch the fuel pellets, one at a time. First it will lauch the fuel pellets needed for deceleration (at 0.1c), then the ones needed for acceleration (at speeds decreasing from near 0.1c to almost 0).
During the acceleration phase, the ship will collect fuel pellets and burn them, in order to accelerate (given that, at any point during acceleration, the ship wwill have ~empty tanks, tha amount of fuel needed to reach 0.1c will be far lower than that would be required by the rocket equation).
In my proposition – the accelerator will have to launch:
-50,000t 1g fuel pellets (at near 0.1c) for deceleration (only this fuel will be accelerated to 0.1c, NOT the ship). These fuel pellets will be fired one at atime; the accelerator can take its time while doing this, because the starship will collect these fuel pellets while it flies at 0.1c (a state which will last most of the journey).
-1g fuel pellets (at speeds varrying from near 0.1c to 0); far less than 50,o0ot, this time. During this phase, the accelerator will work at below its maximum capacity (due to the fact that the fuel pellets will have so low a kinetic energy – if they were not fuel, they would not be enough to propel the empty ship to 0.1c).
After this, the starship will be able to fly with as high an acceleration curve as planned (spending as little time on the journey as possible).
In your proposition, your launcher will have to launch enough kinetic pellets to move the fuelled ship (50,000t+ship) to 0.1c.
If the ship is to have an appreciable acceleration curve, the launcher will have to work much harder than my accelerator (launch either far more kinetic pellets per unit of time or far faster kinetic pellets); the launcher’s performance must be far superior for the same travel period.
Of course, you could choose for the ship to have a low acceleration curve (spending far more time on the journey).
In conclusion- the main problem I see is that, for the same travel time for the starship, your launcher’s performances must be far superior to my accelerator;
There is also the fact that the total kinetic energy your launcher must produce is above the kinetic energy produced by my accelerator (the energy needed to accelerate the empty ship is not given by my accelerator, but by burning fuel pellets which have a lower kinetic energy);
Also – the kinetic pellets will have to impact the ship at high velocity; even if a magnetic field strong enough to shield the ship throughout the journey could be devised (it’s doable), it will mean more mass added to the ship (potentially substantially more).
Eniac
About the magnetic induction accelerator:
You mentioned two main problems:
1 – the magnetic fields must change at just the right time, synchronised;
2- for the same rate of change of the magnetic field (electromotive force EMF), the stationary fuel pellets experience a larger acceleration than the fuel pellets at near 0.1c.
1- the timing of the change of the magnetic fields is a solved problem; it was solved 70 years ago in the case of the betatron.
2-you make an accelerator with the best rate of change of the magnetic fields possible with your technology; the fuel pellets at rest are accelerated more than the fuel pellets at near 0.1c.
You will only have to make the accelerator longer in order to reach near 0.1c with the acceleration’s value decreasing as the fuel pellets’s speed increases.
If 20,000g can reach 10,5km/s in only 1km, with fuel pellets weighing 1g (20,000 times less) needing to reach 30,000km/s (only 3,000 times more), you have a lot of length available before the accelerator becomes impractically large.
Eniac
Also, about the fuel pellets, consider:
I repeatedly said the fuel pellets should weigh 1g.
This is NOT the minimal limit on the fuel pellets’ weight. Indeed, there’s a lot of room to make the fuel pellets even lighter – and smaller – before Heisenberg’s uncertainty kicks in and diffraction becomes a problem.
In the sailbeam proposition, on the other hand, the micro-sails can not be made much lighter than a few grams – they need to have a substantial surface area to enough photons from the super-laser to reach 0.1c.
A significant disadvantage for the sailbeam micro-sails – for any kinetic pellets system.
A magnetic induction accelerator to accelerate fuel pellets ligher than 1g to near 0.1c is FAR easier to build than a super-laser that must accelerate micro-sails many times heavier to 0.1c.
ProtoAvatar: Betatrons have nothing in common with the accelerator you propose. They use rapidly varying electrostatic fields (RF) for acceleration, and a (relatively) *slowly* varying magnetic field to bend the particles in a circle. Neither is applicable for macroscopic objects.
The mass of the projectile does not affect the acceleration or length of accelerator, as you can see from L = 0.5 v^2/a. Given a large magnet, a small nail is not accelerated any more than a large one, because force and mass both depend on size.
Seems I mistook betatron for a cyclotron. Betatrons are limited to one pass through the field, and thus limited by magnetic field strength.
Particle accelerators rely on the charge of particles. They do *not* work for macroscopic projectiles. Let us stop pretending they do.
Not that it matters, because a railgun certainly won’t scale to planetary dimensions, but the current state of the art appears to (at least according to ProtoAvatar) the US Navy’s “Mach 8” railgun, which does “5500 feet/s”, or about 2 km/s. And they are presumably longer than the Yugoslav guns, further reducing the maximum acceleration.
I do not doubt the veracity of the various accounts, I only submit that given hearsay lacking proper documentation it is easy to get some of the numbers wrong. As an example, the 5,500 feet/s do not really match the “Mach 8” in the very same article, or do they?
The 10 km/s number you recall seems to conflict with what appears to be the state of the art in high-speed projectiles, but I could be wrong.
In the Yugoslavian story, what seems most suspicious to me is the 0.7 m length. This is really short for a 3000 m/s gun, and happens to coincide numerically with the 0.7 g projectile mass. Without proper documentation, I would consider these numbers questionable.
Mass drivers other than railguns (with a better chance of being scalable to orbital velocity) have never been built to actually reach km/s velocities, as far as I know, although there seems to be an unusually large hobbyist scene around coil guns.
O’Neills “Mass Driver 1” in 1977 reached an acceleration of 300 m/s^2. Not bad, but not exactly close to what we have been talking about. “Mass Driver 2” was never builts. I am not aware of other attempts.
Found the article, page 78.
http://www.popsci.com/archive-viewer?id=Gr9KVVPcNPYC&pg=78&query=railgun
Yes, it’s not going to scale up to well.
Eniac
About F=ma:
“The mass of the projectile does not affect the acceleration or length of accelerator, as you can see from L = 0.5 v^2/a.”
Are you actually proposing that the same mass driver (same length, same EMF) accelerates a mass of 1g at the same rate as a mass of 100kg?
Eniac, the mass of an object very much DOES affect its acceleration when subjected to a force (any force):
F=ma – when relativistic effects are negligible, which is the case betweeen 0 and 0.1c.
The electromotive force EMF=ma. When the mass is smaller, the acceleration is proportionally larger.
And if the acceleration is proportionally larger, the length of the accelerator can be proportionally smaller for the same final velocity – as per L = 0.5 v^2/a.
Here’s a quote from a Wikipedia link that adresses the reverse proportionality between the mass of the projectile and the acceleration imparted:
http://www.nss.org/settlement/L5news/1980-massdriver.htm
“On the other hand, if the power requirement [for the mass driver] were reduced by a factor of 60, there would be no need for energy storage at all. This could be done either by making the launcher 60 times longer (468km), or by making the vehicle 60 times smaller (17kg).”
Eniac, as per F=ma, by making the object 4 (or 5) orders of magnitude lighter, you increase the acceleration ~4 (or 5) orders of magnitude.
About to the problem:
‘2- for the same rate of change of the magnetic field (electromotive force EMF), the stationary fuel pellets experience a larger acceleration than the fuel pellets at near 0.1c.
2-you make an accelerator with the best rate of change of the magnetic fields possible with your technology; the fuel pellets at rest are accelerated more than the fuel pellets at near 0.1c.
You will only have to make the accelerator longer in order to reach near 0.1c with the acceleration’s value decreasing as the fuel pellets’s speed increases.
If 20,000g can reach 10,5km/s in only 1km, with fuel pellets weighing 1g (20,000 times less) needing to reach 30,000km/s (only 3,000 times more), you have a lot of length available before the accelerator becomes impractically large.’
And, of course, you can make easily make the fuel pellets 0.1g – 200,000 times less than 20kg (that’s 5 orders of magnitude).
An option you do not have with sailbeam’s microsails (aka lenses).
And about ‘changing the magnetic field at just the right time’:
“Seems I mistook betatron for a cyclotron. Betatrons are limited to one pass through the field, and thus limited by magnetic field strength.”
Eniac, what the betatron proves is that is is quite possible to change the magnetic field at just the right time. The timing of the change of the magnetic field is of interest here – and this timing is FAR more precise than would be required to accelerate pellets to only 0.1c:
Betatrons work by magnetic induction – much like the mass driver.
They can accelerate particles to near light speed. At near light speed, 70 year old betatrons had no problem changing the magnetic field at just the right time, everywhere along the accelerator.
Mass drivers that must accelerate fuel pellets to only 0.1c don’t even have to be as precise as the betatraon – not even close.
‘Changing the magnetic field at just the right time’ is a solved problem; it was so for 70 years.
Eniac
“the current state of the art appears to (at least according to ProtoAvatar) the US Navy’s “Mach 8? railgun, which does “5500 feet/s”, or about 2 km/s. And they are presumably longer than the Yugoslav guns, further reducing the maximum acceleration.
[…]
The 10 km/s number you recall seems to conflict with what appears to be the state of the art in high-speed projectiles, but I could be wrong.”
The railgun launched 23 pounds – 10,5 kg – at 5,500 feet/s – 2 km/s.
The previous rail-guns lauched much lighter projectiles – like the 0,7g one for the yugoslavian one – hence the greater velocities.
“Mass drivers other than railguns (with a better chance of being scalable to orbital velocity) have never been built to actually reach km/s velocities, as far as I know, although there seems to be an unusually large hobbyist scene around coil guns.”
I find the mass driver receives very little attention, considering its potential – it could prove to be more viable than the space elevator as a way to reach Earth orbit at low cost, for starters.
The ‘heat by friction with the atmosphere’ problem strikes me as solvable; indeed, it seems to be easier to solve than the problems that need an answer before you could build a space elevator:
http://en.wikipedia.org/wiki/Space_elevator
ProtoAvatar: What you are missing (even though I think I mentioned it) is that in a magnetic accelerator, the force on the projectile depends on its size. Smaller objects experience less force, same acceleration. So, no, you cannot increase the acceleration arbitrarily by making the projectile smaller. You save energy (as per your Wikipedia link), but energy is not the limitation we are discussing here. We were discussing length and acceleration.
There are dozens of other misconceptions in your arguments, but I am getting tired of addressing them all.
Eniac”Because the charge/mass ratio allows us to use electrostatic fields for acceleration, which does not have these problems.”
“Particle accelerators rely on the charge of particles. They do *not* work for macroscopic projectiles. Let us stop pretending they do.”
“Electrostatic fields”, that’s like the static electric fields used to pick up bits of paper or polystyrene balls isn’t it? You can also use them to bend the water flowing from a tap around a plastic rod without actually letting the water touch the rod.
I’d bet money that those charged polystyrene balls could be made to accelerate at at least tens of G’s, in a suitably designed particle accelerator.
I understand the maximum charge/mass is to some extent dependent on the density of the macroscopic object, so if we pick a very low density material optimized to hold the maximum charge/gram perhaps we can get far higher accelerations than Eniac thinks. The accelerations achieved with atomic nuclei seem to be in the hundreds of millions to billions of Gs, so it should be possible to accelerate a macroscopic projectile that had just 0.01% of the charge/mass ratio of such ions at hundreds of thousands of Gs.
Eniac
“ProtoAvatar: What you are missing (even though I think I mentioned it) is that in a magnetic accelerator, the force on the projectile depends on its size.”
Eniac, when making a mass driver for accelerating small, light pellets, you will make the acceleration channel only mm in diameter (the electromagnets are arranged around it), not cm/m in diameter, as you would if you would want to accelerate larger objects.
This means the magnetic flux generated by the electromagnets will be concentrated in that mm thick acceleration path; the change magnetic flux passing through the small pellets will be comparable to the changing magnetic flux passing through larger objects, located in mass drivers with wider acceleration paths.
Meaning EMF will be ~the same.
“You save energy (as per your Wikipedia link), but energy is not the limitation we are discussing here. We were discussing length and acceleration.”
Do read that Wikipedia link, Eniac:
“On the other hand, if the power requirement [for the mass driver] were reduced by a factor of 60, there would be no need for energy storage at all. This could be done either by making the launcher 60 times longer (468km), OR BY MAKING THE VEHICLE 60 TIMES SMALLER (17kg) [this being the requirement for attaining the same final velocity with 60 times less energy and the same length of the accelerator].”
As per that Wikipedia link, with less energy you can accelerate less mass to the same final speed – that would be because a smaller EMF=less mass times the same acceleration.
“There are dozens of other misconceptions in your arguments, but I am getting tired of addressing them all.”
In yours too, Eniac.
Andrew: Why 0.01%? Try something much smaller. I don’t have time to figure it, but I recommend you do before you bet any money.
This is true. My feeling is it is because the hurdles (some of which we have been discussing) are too great to allow viable proposals. It appears the mass driver and space elevator are of similar difficulty.
Ultimately, it is because the energy to get something to orbit is comparable with the energy of chemical bonds. This causes the problem with rockets (need more atoms for fuel than payload), and the space elevator (chemical bonds are not strong enough to keep it from breaking), and likely also the mass driver.
No matter how often I reread it, it still says by making the vehicle smaller you save energy. Which is what I said. I have no idea what you are getting at here.
No, sorry, making a magnet smaller does not increase its field strength, at least not the way you call for.
Would be nice if it did, then we’d be able to get more than a few dozen Tesla, and with much smaller devices. You’d take the current record holder, scale it down a factor of ten, and Voila, thousands of Tesla, on the table-top. Perhaps they just didn’t think of it?
It does work for electrostatic fields, which is why the strongest fields possible are at the tip of an incredibly sharp needle.
Eniac
“No, sorry, making a magnet smaller does not increase its field strength, at least not the way you call for.”
That’s NOT what I was talking about.
Every mass driver must have a pipe through which the object to be launched is accelerated. Only the magnetic field present in this region will affect EMF.
If your pipe is 1cm wide, you can put the electromagets near the pipe closer together than when the pipe is 1m wide (I even checked LHC’s dipole magnets configuration to see if putting closer together 2 strong magnets generates unallowable mechanical stresses too large. The result: the proton beam pipe is 3,3cm diameter; the center of the two 8,3tesla magnets on either side of the beam pipe are ~16cm apart; a non-magnetic laminated alluminium collar – not even thick – is enough to keep them together).
This means the magnetic field strength beween the electromagnets in the 1cm pipe will be greater. Which means, when the magnetic field changes, the change between maximum strength and 0 will be greater for an AC of the same frequency.
This will affect the EMF positively.
That was the point I made in my last post. But there’s a simpler way to prove my point, which is that when making the object to be launched lighter, it is easy to make the EMF NOT decrease (or not decrease at nearly the same rate):
EMF=change of magnetic flux per time; magnetic flux is the magnetic field that passes through an area.
Let’s say we don’t change the magnetic field strength in a pipe with a diameter of 4cm.
First, you lauch an object 10kg heavy. Its diameter is ~4cm; that’s the area relevant for calculating its magnetic flux. Why can’t we make this are wider? because then, we’ll have to enlarge the pipe with negative consequences for the magnetic field in the pipe – you’ll never see such a pipe with a diameter of ~100m without some truly large electromagnets.
Now let’s take an 1kg object. Let’s make him ring-shaped/domut shaped. Its area relevant for calculating its magnetic flux will be disproportionately large by comparison to the 10kg heavy object – indeed, it can easily be made to be equal to the area of the 10kg object.
Same change in magnetic flux per same time gives the same EMF.
But EMF=ma; meaning, for the 2kg object the acceleration will be 10 times greater.
To conclude, it is easy to modify the shape/area of an object, increasing the magnetic flux (magnetic field passing through that area); easy to keep EMF at the same value by changing the shape of a lighter object.
It is quite impossible to modify the mass of an object.
“No matter how often I reread it, it still says by making the vehicle smaller you save energy. Which is what I said. I have no idea what you are getting at here.”
The author said that for a mass driver of the same length, for the same final velocity, accelerating a mass 60 times lighter ‘costs’ 60 times less energy.
Same length, same final velocity means same acceleration.
60 times less energy means that the EMF will be 60 times smaller, yes, but the mass is also 60 times lighter so, per f=ma, the acceleration remains the same.
Edit:
I wish to correct a typo:
In my previous post, I said –
“Same change in magnetic flux per same time gives the same EMF.
But EMF=ma; meaning, for the 2KG OBJECT the acceleration will be 10 times greater.”
That should be “1kg object”.
EMF is not the force on the projectile, and EMF is not m*a.
EMF (http://en.wikipedia.org/wiki/Electromotive_force) is the strength of an induced electric field in a coil when the magnetic field changes, as it will when a magnetized pellet passes through. To accelerate the object, the EMF must be resisted, otherwise the induced current will suck the projectile right back in, i.e. any acceleration upon approach to the coil will be negated upon leaving. At orbital velocity, the EMF is close to the breakdown voltage of insulators, which is why it is so difficult to use EM acceleration at such high velocities. A smaller projectile will not change this.
We see here the same connection to chemical bond energies as in rockets and space elevators: The EMF limit is dictated by the energy it takes to rip electrons from their places in an insulator, which is of the same magnitude (~1 eV) as chemical reaction (rocket) or bond strength (space elevator).
This also explains why the mass driver limits we have heard about concern the SCR, the semiconductor component which is supposed to shut off the coil current right when the projectile passes. If the projectile is too fast, the EMF blows out the SCR. This limitation is NOT easily overcome. If the projectile is fast enough, it will blow out anything made of matter. This limiting velocity is on the order of orbital velocity, not coincidentally.
You could try to use electrostatic forces instead, but those are very weak for large objects. Somewhere I read (Eric Drexler, was it?) of such a concept, a nano-accelerator that would accelerate interstellar nano-probes electrostatically. The thing was essentially an over-sized Linac. Oversized as in the same range we have been talking about: Millions of kilometers. The need for oversize compared with conventional particle accelerators can be understood as a direct consequence of the MUCH smaller charge/mass ratio that can be achieved with macroscopic objects, even nano-particles.
I am also thinking that probably there is a similar limitation based on breakdown voltage for this one (it would only be fair…), but I do not have a good feeling for how that would manifest itself. Of course, nano-probes would have no chance against erosion by the oncoming ISM, even if you could accelerate them to 0.1c.
Eniac
ANY force F=ma. EMF experienced by an object equals EMF=ma.
EMF experienced by an object also equals EMF=change in magnetic flux per time; magnetic flux being magnetic field times the area the object presents to this magnetic field.
Two objects with the same area, through which passes the same changing magnetic field will experience the same EMF.
But if an object is is twice lighter than the other, the acceleration experienced by the first object will be twice higher.
Notice – for the same change in magnetic field the lighter particle will be accelerated twice as fast.
For the maximum change in magnetic field the SCR (essentially, a switch in the circuit) can support before blowing up due to the current induced in the circuit (by this changing magnetic field), a pellet weighing 1g will be accelerated 20,000 faster than an object weighing 20kg – provided the area both projectiles present to the changing magnetic field (the magnetic flux) is the same (the EMF will be the same for both objects).
Eniac
Yes, the same change in the magnetic field will generate a smaller EMF when the projectile has a high velocity, but that only means the mass driver will have to be longer to compensate.
Given how effective the mass driver is for light particles at more-or-less small speeds, one has a lot of length to spare.
Let’s take a single electromagnet whose magnetic field changes at the same rate:
For a projectile that flys by in 1 second, the difference between the maximum and the minimum values for the magnetic field will be 10 times greater than for a projectile that flys by in 0.1 second. This means the EMF will be 10 times smaller – but there will be no breaking of the object, only a smaller acceleration value.
Your comments indicate a complete lack of understanding the nature of EMF and the problem with it. Blame it on a misnomer, the EMF is not really a force, it is more of an “induction potential”. A force not on the projectile, but on surrounding charges.
As for dealing with “only longer”, try calculating the length of your accelerator when acceleration is not constant, but decreases in proportion to velocity. You will go from “merely” 9,000,000 km or so to some REALLY obscene numbers. Try it.
Eniac
An object displaying a changing magnetic – let’s say, growing in strength – produces in another object an induced electrical current; this electrical current generates a magnetic field of opposite polarity in this second object; these magnetic fields repel each other (the objects are traveling through space accelerately) AKA the objects displaying these magnetic fields are experiencing a FORCE (as per the definition of the force) equal in value, oppsite in sense.
This FORCE (let’s call it, EMF) depends on the rate of change of the magnetic field, the area the objects display to the magnetic field and the time. This FORCE is what spins the rotor in an electric engine, Eniac.
And this force als0 equals ma – as any other force, Eniac.
You do realise Newton obtained this formula by observing forces generated by the electromagnetic fundamental interaction, yes?
“Your comments indicate a complete lack of understanding the nature of EMF and the problem with it”
You’re talkinng about your comments, Eniac.
“You will go from “merely” 9,000,000 km or so to some REALLY obscene numbers.”
First – the 9,000,000 I wrote is an acceleration -m/s^2 – NOT a length.
Second:
“A 1 km long mass driver made of superconducting coils can accelerate a 20 kg vehicle to 10.5 km/s at a conversion efficiency of 80%, and average acceleration of 5,600 g” – I gave this quote earlier.
‘average acceleration’ is 5,600g AKA 56,000m/s^2 at 5.3km/s
At ~5.3km/s, a 20,000g object is accelerated at 56,000m/s^2 by EMF, in a feasible mass driver, with an accesible change rate of the magnetic field.
At 5.3km/s, an 1g object will be accelerated at 1,120,000,000m/s^2, in a mass driver with the same rate of change of the magnetic field.
At 53,000km/s – that is ALMOST 0.2c – , an 1g object will be accelerated at 112,000m/s^2.
The average acceleration for an 1g object along this mass driver will be 11,200,000m/s^2.
Now – ‘l=o.5v^2/a’ – for V=53,000km/s – ALMOST 0,2C!
L=125,401,785M=125,401KM – NOT EVEN 1,000,000KM! NOT EVEN CLOSE!
And remember, this is for a final particle velocity of 0.2c.
For 0.1c the mass driver will only have to be half as long – NOT EVEN 100,000km!
No, let’s not, because it isn’t. This FORCE is not the emf I was talking about, the one I linked you the Wikipedia article and explained all about, the one you did not bother to try and understand the problem with. This FORCE is something else entirely.
The 9,000,000 km I was talking about was the extrapolation of the 1 km mass driver for ~10 km/s to 0.1 c (30,000 km/s). 3,000 times the velocity means 9,000,000 times the length, at the same acceleration. I apologize if I did not make it clear that I was talking about length, not acceleration.
That would be nice. Alas, it is not true, since the 1 g object will of course have a much smaller magnetic moment than the 20 kg object, ensuring that the FORCE (which has nothing to do with emf) will be proportionally smaller. Since the magnetic moment scales with the volume of the object (most often an aluminum ring, but it might also be a permanent magnet or a superconducting coil), the acceleration will be the same, regardless of size.
It appears that you are forming your average by taking the geometric mean of the initial and final accelerations. This makes no sense whatsoever. What you are looking for is the time average, which is dominated by the final acceleration in this case, because most of the time is spent where acceleration is low.
After you correct for the last two mistakes, you will get numbers that are closer to the truth. Approximately, the acceleration at 10 km/s is 56,000 m/s^2, that at 0.1 c is 20 m/s^2, and the average is also around 20 m/s^2. The length then comes out at 45,000,000,000 km. Much shorter than I had expected, actually. I think the assumption that acceleration is inversely proportional to velocity is in our favor, and not correct. More likely it peters out at a higher power or even exponentially.
“Since the magnetic moment scales with the volume of the object (most often an aluminum ring, but it might also be a permanent magnet or a superconducting coil), the acceleration will be the same, regardless of size.”
I already explained to you how THE AREA (VOLUME) OF AN OBJECT CAM BE EASILY MANIPULATED – ENLARGED (unlike its mass); for an easy example, making an object of 1 kg donut-shaped, in order to have the same area as an objrect of 10 kg – meaning the force exerted in both will be the same in the same mass driver; the acceleration, however, will be 10 times greater for the lighter object.
The only thing you have to worry about is the electrical resistence.
This means 1g object, at 5.3km/s will be accelerated at 1,120,000,000m/s^2, when a 20 kg object with the same area will be accelerated at 56,000m/s^2.
And at 53,000km/s – that is ALMOST 0.2c – , an 1g object will be accelerated at 112,000m/s^2.
“It appears that you are forming your average by taking the geometric mean of the initial and final accelerations.”
I took the ‘initial’ acceleration at 5.3km/s, instead of almost stationary, and the ‘final acceleration at 53,000km/s, insead of 30,000km/s.
Both assumptions severely in my disadvantage.
“What you are looking for is the time average, which is dominated by the final acceleration in this case, because most of the time is spent where acceleration is low.”
Eniac, an object will go through all velocities.
The final section of the accelerator will have to be longer – but equipped with smaller electromagnets (aka the ‘strongest’ magnetic field they can produce is not very strong)?
The initial section will be extremely short – and equipped with larger electromagnets.
If we take only the final acceleration (112,000m/s^2) for the entire mass driver – an absurdly disdvantageous assumption (which does NOT happen), the length for this 53,000km/s – 0.2c – final velocity mass driver is L=112,540,178KM.
And, by following the same assumption, if we make the final velocity only 30,000km/s we’ll have the final acceleration ~200,000m/s^2. And we’ll have the length of the mass driver ~70,000,000KM.
A mass driver ~70,000,000km.
Only at the start would there be large electromagnets. At the end, the electromagnets will be small (the mass driver being,perhaps, ~20 cm in diameter).
Why? Because, in the time the projectile flys by the electromagnet, the magnetic field will only have time to increase from 0 to a small value.
It’s still rather long.
The mass driver accelerates projectiles effectively when said projectiles fly at low speeds. Only after that the SCR problem becomes significant.
For this portion of the mass driver, the SCR problem would be a lot less sever if you would accelerate the electric circuit that surrounds the electromagnets.
This would mean you’ll have to replace this electric circuit with a series of rings made out of coiled cuperconductor wire, containing SCRs and a power supply, rings that are themselves accelerated by the mass driver (of course, you won’t accelerate them to 0.1c, but as fast as possible; the faster, the shorter the accelerator).
Only after you’ve sent these rings will you start to accelerate the fuel pellets.
I should have emphasized “geometric”. Please justify why you chose the *geometric* mean for your “average”, not the arithmetic or harmonic.