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*To*: starship-design@lists.uoregon.edu*Subject*: starship-design: Current for electric retro-thruster for sail*From*: DotarSojat@aol.com*Date*: Thu, 26 Sep 1996 03:45:26 -0400*Reply-To*: DotarSojat@aol.com*Sender*: owner-starship-design

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

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