# starship-design: Current for electric retro-thruster for sail

```Hi all

On 9/20, Kelly wrote (regarding my note "Deceleration of sail
pushed by constant-power beam"),

>If we assume electric acceleration of the particals, thats also
>very effocent, but how large a drive system would we need to get
>that degree of acceleration?

The efficiency of accelerators that I was familiar with as a
graduate student was not very high; a 1 microamp proton current
at 30 million volts (30 watts output) was the best I can remem-
ber, while the input power was about 300 kilowatts.  This gives
an efficiency of only 0.01 percent.  (Even if my memory is off
by 2 orders of magnitude the right way, the efficiency would
still be pretty poor by our standards.)  For nuclear-research
accelerators, there never has been a strong need for high
current; a microamp gives lots of particles.  Some of you may be
more familiar than I am with contemporary accelerators.

We can calculate the proton current required to give an apprec-
iable thrust from relations in my 9/20 note.  Using the notation
from that note, the relation for the received power is
Pr = Mo * ao * c * exp(-theta)   ,

and the exhaust power, Pex = i * V (current times voltage), is
given by (note: for ao = 1 g, ao * c = 2,940 Mw per kg thrust)
Pex = eta * Pr
= eta * Mo * ao * c * exp(-theta)
= eta * Mo * (2,940 Mw/kgT) * exp(-theta)   .

Now the exhaust power will be increasing as theta is decreasing,
in the deceleration phase, until the maximum allowable deceler-
ation of 1 g is reached.  Thereafter the power will be decreased
by furling the sail as the mass decreases, to keep the deceler-
ation at 1 g.  The maximum exhaust power will therefore occur
just as the deceleration reaches 1 g while the sail is still
fully open.  For the tau Ceti mission-history tabulated in my
9/20 note, the value of theta when 1 g is first reached is about
0.78.  For eta = 1.0, the maximum proton current, i, for the cal-
culated required proton energy of 1060 million volts, is
i = [Mo * (2,940 Mw/kg) * exp(-0.78)]/1060 megavolts
= 1.27 amps per kg of initial sail/ship mass * Mo   .

So, we're talking about roughly 1 amp of 1 GeV protons for each
kg of initial sail/ship mass.  That current is to be compared
with the approximately 1 microamp of proton-accelerator current
of today's state of the art.  (Check that value; I'd be
surprised if you find much higher currents than 1 microamp at
1 GeV today.)

So, we need remarkable progress in improving both proton current
and conversion efficiency before we can count on the beam-driven
sail (or any other propulsion system requiring an electric
thruster).  I need to take another look at electron accelerators;
they can produce much higher currents.

Rex

```