starship-design: Re: Protons vs Electrons for Relativistic Electric Thrusters

[TLG.van.der.Linden@tip.nl (Timothy van der Linden)]

Rex writes at 2/4:

>So, I boil down these points to a single question:
>
>Q: What is the optimum (minimum-antimatter) performance of an
>antimatter-powered starship with its exhaust composed of
>accelerated PROTONS (with electrons dumped for charge
>neutralization), in comparison with that of one with its exhaust
>composed of accelerated ELECTRONS (with protons dumped at
>negligible velocity for charge neutralization)?

Still other ions may work as well depending on optimal exhaust velocity and
"energy" of the accelerator.
I compared the electron-dumping with no-dumping numbers and as expected the
values differ very little.

>ACCELERATED ELECTRONS
>
>The calculational procedure described in my 4/4/96 note has been
>expanded to include dumping of mass at negligible velocity to
>bring about charge neutralization (as well as to include
>conversion efficiencies less than 1.0).
>
>The comparable results of the calculations for accelerated
>ELECTRONS (with dumping of one proton at negligible velocity for
>each electron for charge neutralization: "DUMP = 1836.") are as
>follows with the same nomenclature as above:
>
>Antimatter conversion efficiency = 1.0
>
>  Uend  Vend optVexh  optUexh  maxeff minMam/Mbo minMam/Mi Mi/Mbo
>  0.2  0.196  1.000  0.184E+06  0.090   0.110     0.0900    1.22
>  0.5  0.447  1.000  0.478E+06  0.191   0.309     0.1908    1.62
>  1.0  0.707  1.000  0.931E+06  0.293   0.708     0.2927    2.42
>  2.0  0.894  1.000  0.163E+07  0.382   1.620     0.3817    4.24
>  3.0  0.949  1.000  0.217E+07  0.418   2.584     0.4186    6.17
>  4.0  0.970  1.000  0.257E+07  0.438   3.565     0.4382    8.14
>  5.0  0.981  1.000  0.289E+07  0.450   4.554     0.4503   10.11

I'm amazed that dumping so much mass can still give efficiencies over 25%.

>For electrons, there is no maximum efficiency as a function of
>Uexh for finite values of Uexh; the efficiency increases
>monotonically as Uexh is increased.  The maximum is replaced by an
>asymptote at infinite Uexh.  The value of "maxeff" tabulated above
>is that efficiency when the increase in efficiency is 0.001
>percent for an increase in Uexh of 1 percent; the tabulated value
>is within about 0.1 percent of the asymptote.

I assume that the meaning of optUexh has the same origin?

Since you propose that infinite exhaust speeds are the best, isn't Steve
right saying that you could better use photons as propulsion?

>COMPARISON

>For the electrons' "optUexh" of 0.289E+07 ltyr/yr for the Uend of
>5.0 ltyr/yr, the ELECTRON accelerator energy is about 1,480 GeV. 

I've a book from 1991 that says: "Several accelerators now exist capable of
producing electron and positron beams of energies up to 50 GeV (and higher
in the future)...."
[I assume the accelerators aren't linear ones!]

Also Ken's note about 60 GeV/m over 1 mm does seem far away.

>The thrust T is given by the relation
>     T = iV sqrt[1 + (2mc^2/eV)] * (1 kgf/2,940 Mw)  ,
>
>where mc^2 is as above, i is current in amps, V is volts and
>eV is the accelerator energy in MeV; 1 amp*volt is 1 w.
>
>The values extracted from the Uend = 5.0 lines in the tables
>above or calculated from the above relations are as follows:
>
>   Property           Proton exhaust    Electron exhaust
>  Mass ratio              15.11              10.11
>  Maxeff                  0.610              0.450
>  MinMam/Mbo              3.357              4.554
>  MinMam/Mi               0.2222             0.4503
>  Accelerator Energy (Mev) 850.            1,480,000.
>  Thrust/amp (kgf)        0.520               500.
>
>"You pays your money and you takes your choice."

1000 times lower currents, 1741 times lower voltages and higher efficiency
seem strong enough reasons to me to choose for proton exhaust. The 50%
bigger mass ratio is almost neglectable compared to the advantages.

Timothy