http://forum.nasaspaceflight.com/index.php?topic=29276.msg1285083#msg1285083 continued
@John & JP hope this will indirectly address your remarks, can answer more specifically if more clarifications needed.
The following reading is a little bit paranoid, and might see more intent than there really is...
So far, the offending Appendix A has stated that something fishy is going on about energy conservation with propellantless schemes. There should be some correction term depending on speed (relative to what is still unclear). Not stated : for energy conservation the correction would be severe, but we won't try to see how it would affect our fast trajectories (main body of paper). We are given a chart comparing various Thrust/Power ratios to see that from this point of view a Q-thruster is comparatively only an improvement on a Hall thruster, same ballpark just about one order of magnitude better. No crazy values, Hall thrusters are proven, and we are not pretending to be a million time better. What we are to think of the fact that on the vertical axis the Hall thruster has a higher "Delta-V Limit (absolute frames)" is left uncommented. For action/reaction scheme this "Delta-V limit" is of the same order as the ejection speed, and of the same order as the delta-V achievable through reasonable dry/wet mass ratios. For a propellentless scheme the dry/wet ratio is 1 for all practical purpose, so either the thrust/power don't care about "absolute frames" and this Delta-V limit is irrelevant (and energy is "tapped" from somewhere), or it does care about (for some unclear reason) and then at face value it means it is worse than Hall thruster for high delta V missions.
Instead of clarifications we have a mystification :
<<At this point, it is a useful exercise to explore this issue from a relativistic point of view, as it will uncover a paradox.>>And then we will be shown that something fishy is going on
also with a theoretically sound action/reaction system like a Hall thruster spacecraft. And the Appendix will conclude that
<<Although the example mission (with a Hall thruster)
is clearly not an exotic mission and can easily be achieved in practice, the point of this paragraph is to identify that the paradox can be created for any spacecraft using conventional propulsion as well as advanced propulsion.>>There we are : this is not a paradox or a problem with propellentless schemes, this is a paradox inherent to
any spacecraft when energy is accounted for in an inertial frame fast enough relative to those typical delta Vs, because any of those has a Ts such that 1/Ts < high speeds, so surely any spacecraft can (apparently) provide more energy in kinetic form than is spent by the onboard generator.
This is not a paradox with Q-thrusters, this is a paradox with relativity of velocities and how kinetic energy is accounted for in different inertial frame (we all know this is a messy business with all this square thing and non additivity...) For instance, thought experiment, say we have a thruster at 0.05 N/kW that has a 1kW onboard generator, pushing at constant 100km/s relative to a device that receive mechanical energy (from this push) and converts it to electric energy. Then the mechanical energy received by this device is Force*speed = 0.05*100000=5kW. Surely this is enough raw mechanical energy to feed back 1kWe to the thruster ! Silly isn't it ? Note that : I didn't made any assumption on to what kind of thruster was used, the same calculations would hold for any thruster with 0.05N/kW thrust/power ratio.
We are left with this paradox, which plagues
all spacecrafts when considered in some inertial frame fast enough. Surely there is some explanation everyone knows (so it's not worth talking about). Or maybe there is a deep mystery still lurking within Newtonian mechanics (so it's not worth talking about in an Appendix). But for sure Q-thruster is no fundamentally different from Hall thruster in that matter.
The peculiar velocity of our local (I mean, you know, a
real velocity) relative to CMB as a preferred natural cosmic rest frame is just a gizmo to add to the mental confusion. Are we to understand it is important to find a real velocity or a natural rest frame ? This is left to the uncertainty of the reader... Fact is : take any arbitrary inertial frame with velocity>100km/s aligned with spacecraft trajectory will do the same job. Such that from this "absolute frame" a spacecraft at rest in its local frame (on its launch pad) has already 100km/s before it adds another km/s on the cheap (from its point of view) to a staggering 101km/s, and yet it would in principle take more energy to go from 100 to 101 than to go from 0 to 1. Because of the square.
100² to 101² -> needs to add 201
0² to 1² -> needs to add 1
Wow, again, seems paradoxical, as this is the same "thing", just seen from a different way...
So we have this
artefact of relativity and kinetic energy accountancy. Let's live with it and see how the quantum vacuum can be modelled as a plasma we can push on...
But not so fast ! Nature is not an accountant that can be fooled around. We are given a numerical example to be convinced. The numerical example is given
for Hall thruster (the thing that is serious) and we will see, again, this paradox.
<<The initial mass is 10,000 kg, the final mass is 9,460 kg. The initial velocity is 371 km/s, and the final velocity is 372 km/s.>> <<The amount of energy provided by the power source over this time frame is 174 Gigajoules.>>We are invited to do
<<The change in kinetic energy as measured by the inertial observer at rest relative to the background radiation is the initial kinetic energy 1/2 mi vi² minus the final kinetic energy 1/2 mf vf² .>>And see that the result is
<<The change in kinetic energy is 33,649 Gigajoules, which is two orders of magnitude larger than the energy provided by the power system.>>Do the math, see for yourself, that works.
Except for one point : since when do you measure a change by subtracting a final amount from an initial amount ?Proper handling shows that we are not gaining but losing : EKf-EKi = - 33649 GJ (minus)
How comes ? Because we are losing mass ! Hall thruster is an action/reaction scheme.
The dry mass fraction of 9460kg has more kinetic energy at 372km/s than at 371km/s
But the wet mass at 371km/s as more kinetic energy than the dry mass at 372km/s
So far we are nowhere near gaining more net energy than spent.
If we are to take into account the kinetic energy of the expelled mass of 540kg with Isp 1838, that is ejection velocity around 18km/s, from 371.5 on average, speed of expelled mass drifting behind is 353.5km/s :
Total kinetic energy initial
.5*10000*371000²
= 688205000000000
Total kinetic energy final
.5*9460*372000² + .5*540*353500²
=654556320000000 + 33739807500000
= 688296127500000
Change in kinetic energy :
final - initial
= + 91127500000 = 91.1 GJ
So we gained 91.1 GJ while
<<the power source over this time frame is 174 Gigajoules.>>There is nothing fishy going on with a Hall thruster.
On the other hand,
with a Q-thruster of same Ts=0.056N/kWe which is
not expelling mass, for roughly the same result, 10000kg*1000m/s=1e7 momentum will use E=1e7/Ts=178 Gigajoules (a bit more than Hall thruster since the spacecraft doesn't get lighter on the way) from onboard power source.
Total kinetic energy initial
.5*10000*371000²
= 688205000000000
Total kinetic energy final
.5*10000*372000²
=691920000000000
Change in kinetic energy :
final - initial
=3710 GJ
About 20 times more than spent.
There is something fishy going on with a Q thruster.
The same remarks would apply for any arbitrary rest frame : the sane system (Hall thruster) will
never exhibit more kinetic energy change (final - initial) than spent energy.
The pathological system (Q-thruster) will sometimes exhibit more kinetic energy change than spent energy, sometimes less, depending on arbitrary frame from where kinetic energy is measured.