Nuclear powered VASIMR and plasma propulsion doable now, Page 3: High efficiency conversion enables zero radiator mass.

Copyright 2015 Robert Clark

Low Radiator Mass at High Efficiency.

 Discussions on various forums have argued the point that actually low conversion efficiency is preferred to save on radiator mass. The idea behind this is that by the Stefan-Boltzmann Law, energy is radiated away according to the fourth power of the temperature. So high thermal energy conversion efficiency resulting in low output temperatures would require larger radiators than with low conversion efficiency with high output temperature. This is explained on this page:

Heat Radiators.
"As an example of the severity of this problem, let us examine the case of a
simple nuclear power plant whose energy conversion efficiency from thermal
to electric is approximately 10 percent. The plant is to generate 100 kW of
useful electricity. The reactor operates at approximately 800 K, and a
radiator with emissivity equal to 0.85 would weigh about 10 kg/m2. The
thermal power to be dissipated from the reactor would be about 1 MW. From
the Stefan Boltzmann Law, the area of the radiator would be about 50 m2 and
the mass approximately 500 kg. This seems quite reasonable.
However, we must assume that the electricity generated by the power plant,
which goes into life support systems and small-scale manufacturing, would
eventually have to be dissipated also, but at a much lower temperature
(around 300 K). Assuming an even better, aluminum radiator of about 5 kg/m2,
with again an emissivity of 0.85, in this case we find that the area of the
low temperature heat rejection component is 256 m2, with a mass approaching
1300 kg."
http://www.projectrho.com/public_html/rocket/basicdesign.php#radiators

 This web site by the way provides a nice collection of the work that has been done on advanced space propulsion systems.

 An additional problem though in regards to low efficiency conversion is that you need higher mass for the reactor and larger amounts of radioactive material that needs to be launched to orbit. For example in the blog post:

"Nuclear powered VASIMR and plasma propulsion doable now, Page 2,"
http://exoscientist.blogspot.com/2015/10/nuclear-powered-vasimr-and-plasma.html ,

I suggested running the reactor at low power to extend the lifetime. In this mode the reactor weighing 2,200 kg would put out 8 megawatts using 200 kg of uranium fuel. If instead of the high conversion efficiency I was aiming for, we selected 10% conversion efficiency, we would need a 10 times larger reactor and 10 times more radioactive fuel. This would put the mass of the reactor at 22,000 kg and the uranium fuel at 2 tons.

 There might be some methods to reduce the heat that needed to be radiated away in the high efficiency scenario. For example Stirling engines can operate even at low temperatures. We could use these to make use of the heat at low temperatures coming from the turbines of  our generator.

 There is also research on lightweighting radiators such as by using carbon-carbon composites:

High Conductivity Carbon-Carbon Heat Pipes for Light Weight Space Power System Radiators.
NASA/TM—2008-215420
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20080045532.pdf

 However an interesting possibility exists that we might not need any radiators at all for the high efficiency case. 

  In the high efficiency case at low output temperature, you can bring the output of the working-fluid down to cryogenic temperatures, as for example for a de Laval nozzle exhausting out to vacuum. If the electric generator equipment is at room temperature, or chilled to decrease resistance and therefore increase power output and specific electric power, then we can have the working-fluid output temperature be lower then the electric generator equipment. So it can used to remove the heat given to the electric generator due to small proportion of thermal not converted to electric power.

 Note this would not obtain for the low efficiency, high output temperature case. If the output is at, say, 800 K to 1,000 K, then by the Second Law of Thermodynamics (Clausius form) we could not use this to cool the generator operating at, say, 300 K or below.

 However, by exhausting down to cryogenic temperatures we could use the cold working-fluid to cool the generator. 

 We need also to cool the turbine. Turbines can be at 90%+ efficiency. The turbine however will be receiving the working fluid at the output temperature. We can though allow the working-fluid to expand further after exiting the turbine to drop to a lower temperature. This then could be used also to cool the turbine.

 An additional factor to provide cooling are the nozzle extensions used for high expansion ratio upper stage engines. For example the RL10-B2 nozzle extensions increase the area ratio to 285-to-1.

https://web.archive.org/web/20160420192309/http://www.b14643.de/Spacerockets/Diverse/P&W_RL10_engine/RL-10B-2-1a.jpg

 The nozzle extension doubles the weight of the RL10 engine from 150 kg to 300 kg, so weighs 150 kg. The upper part of the nozzle is regeneratively cooled but the carbon-carbon extension is only radiatively cooled. The RL10-B2 engine puts out ca. 250 MW of power measured by its 110 kN thrust and 465.5 s Isp. 

 Because of the low mass of the spacecraft due to the short travel time the power level for the plasma propulsion can be less than 10 MW. Then, with regeneratively cooled upper nozzle section, the nozzle extension to bring the exhaust output down to cryogenic temperatures for this power level might only be 1/25th as large, so only 6 kg(!)

Correction to fuel replacement mass.

 In the comments section to the "Nuclear powered VASIMR and plasma propulsion doable now, Page 2" post, Rok Adamlje noted that my estimate for the fuel canister mass that needed to be replenished was too small. I was taking it to be just the uranium fuel mass when the actual total canister mass may be ten times higher.

 In the section there titled, "Long Life by Multiple Nuclear Fuel Canisters", I calculated the average specific power when using 468 fuel canisters at 200 kg each to last the 39 days of the flight. If we take the fuel canisters instead to be 2,000 kg then we can still get high average specific power by jettisoning the used canisters: 

 The rest of the engine mass, which will be fixed, is a small proportion of the total mass of the fuel canisters so we'll calculate the average specific power based on just the total fuel canister mass. The average specific power will be:

  545 MW       545 MW                  545 MW         545 MW

 ------------ +  --------------- + ... +  -------------  +  -------------

  468*2,000      467*2,000                2*2,000          1*2,000

-------------------------------------------------------------------------

  468

545MW     1               1                    1            1

 --------- (-------- +    ------- + ... +  --------  +  -------)

  2,000       468          467                  2            1

=  ----------------------------------------------------------------------

         468

 The summation in the numerator is the sum of the reciprocals of the natural numbers and is well approximated by the natural log function ln(n). So this will be:

(545,000,000/2,000) *(ln(468)/468) = 3,580 W/kg, still above the 1,000 W/kg level needed for the plasma propulsion.

 Note though the length of time the engine will need to be run is actually less than 39 days because of the small mission size due to the fast travel time. So we'll need fewer replacement fuel canisters and the actual average specific power will be greater.

 Also it could be much of the canister(s) can be reused, primarily replacing just the uranium fuel. This will also increase the average specific power.

      

        Bob Clark

Nuclear powered VASIMR and plasma propulsion doable now, Page 2.

Copyright 2015 Robert Clark

 In the blog post "Nuclear powered VASIMR and plasma propulsion doable now", I argued that nuclear space reactors already have the capability to do fast transit times to Mars using plasma propulsion systems such as VASIMR or Hall effect thrusters.

Low Power Operation for Long Life.
 However, there was a key fact left out of that analysis: when space nuclear reactors are run at full power they only have limited lifetimes, measured in hours:

Bimodal NTR.
Engine (Thrust Mode)
Thrust per engine 67,000 N
Total Thrust 200,000 N
T/Wengine 3.06
Exhaust Velocity 9,370 m/s
Specific Impulse 955 s
Propellant
Mass Flow 7.24 kg/s
Full Power
Engine Lifetime 4.5 hours
Reactor Power 335 MWthermal

http://www.projectrho.com/public_html/rocket/realdesigns.php#bimodalntr

 This is alright for the applications usually thought of the nuclear rocket engines where they are used only for a few minutes for takeoff and landing.
 But for plasma propulsion as with other types of electric propulsion they achieve high speeds by running them continually for days. Note though that in examples such as the Bimodal nuclear thermal rocket (NTR), they have two modes of operation, a propulsive mode at full power, and an electricity generator mode at greatly reduced power.
 It is in the low power, electricity generator mode that they can run for months to years. Then one idea to deal with the short lifetime at full power is to run the engines at an intermediate power level that will allow them to run for just the few days needed for plasma propulsion.
 We'll use this report to estimate the possible run-times when operated at lower power:

A One-year, Short-Stay Crewed Mars Mission Using Bimodal Nuclear Thermal Electric Propulsion (BNTEP) - A Preliminary Assessment.
http://ntrs.nasa.gov/search.jsp?R=20140009579

 This report is interesting in that it uses the nuclear thermal engines for high thrust maneuvers such as Earth departure and slowdown at Mars arrival, and electric propulsion for the long interplanetary traverse to Mars. I envision as well low thrust electrical propulsion would be best utilized if they spacecraft is sent far outside Earth's deep gravity well by either chemical or nuclear thermal propulsion before the electrical propulsion system is turned on.
 The full power level for the engines used in the report is 545 megawatts thermal for each of the three nuclear engines, at a weight of ca. 2,200 kg each. They would only be run at full power for less than two hours however. Most of the trip the engines would be run in low power mode:

 For the 1-year round trip BNTEP mission, the total operational time for the BNTR engines is 324 megawatt - days (MWD) which includes 1.75 hours of high thrust / high power mode operation totaling 40 MWD and 284 MWD of reduce power EP mode operation. Assuming 1.2 grams of U-235 consumed per MWD, the total U-235 fuel loss in each engine is 389 grams. Since each cermet fuel BNTR has in excess 200 kg, the burn-up is less than 0.2% which is quite acceptable.
A One-year, Short-Stay Crewed Mars Mission..., P. 7.

 Then to get a maximum of 324 megawatt-days while using it only in the long life, low power mode for say a 39 day flight time, that would correspond to a power level of 8.3 megawatts for each engine. At a weight per engine of 2,200 kg, that corresponds to a specific power of 3,800 watts thermal per kilo.

Long Life by Multiple Nuclear Fuel Canisters.
 The above method would be to run the engine just at much reduced power to get the long life. Another method would be to run the engine at full power but just have multiple nuclear fuel canisters that can be used when one gets depleted. The mass of the fuel as given in that passage above from "A One-year, Short-Stay Crewed Mars Mission", page 7 is 200 kg. The run time for the engine at full power is given in that report as 2 hours. Then for a 39 day run time you would need (24/2) * 39 days = 468 fuel canisters, for 468 * 200 kg = 93,600 kg. Plus the 2,200 kg for the engine this would be 95,800 kg for the nuclear power system. Since in this case the engine is always running at full power this would be 545,000,000 W/95,800 kg = 5,700 watts thermal per kilo specific power. You could improve the average specific power perhaps by a factor of 2 by jettisoning the depleted fuel canisters.

Short Flight Time Actually Gives Smaller Mission Size.
 Actually in a follow up post I'll discuss the specific power is actually higher in both these methods because the engines will not have to be run the entire 39 days to get the high delta-v needed for the short flight times. The main reason is you can use a much smaller habitat perhaps only 6 metric tons when the flight time is only about a month compared to the 25 metric tons or higher usually estimated for a 6 to 8 month flight time. I discuss this in the blog post, "Propellant depots for interplanetary flight." This then would translate into a smaller fuel load and shorter burn time.

 In fact, the surprising conclusion you get is the short flight time requiring high delta-v results in a smaller mission size.

Efficiency of Conversion to Electrical Power.
 Remember to get VASIMR or Hall effect thrusters at the 39 day flight time, we only need 1,000 watts per kilo as discussed in "Nuclear powered VASIMR and plasma propulsion doable now". But this has to be electrical power, not the thermal power of the NTR's. To get the conversion of the thermal to electrical power, I suggest turbines modeled on the Space Shuttle SSME's hydrogen turbopumps. These have a remarkable power to weight ratio of 150,000 watts per kilo, and efficiency of 80%:


Space Shuttle Main Engine Orientation.
http://large.stanford.edu/courses/2011/ph240/nguyen1/docs/SSME_PRESENTATION.pdf

 The "turbine efficiency" in the table is the isentropic efficiency. This is the percentage of the ideal efficiency possible with no loss of heat or friction losses. But what we really need to know is the thermal efficiency, the percentage of the thermal energy converted to mechanical power by the turbines.
 Note that the thermal efficiency is limited by the Carnot limit, dependent on the temperature of the thermal source compared to the temperature of the outlet. For the SSME turbopumps the temperature drop is not very large, necessitated by requiring high pressure for injection into the combustion chamber:

 However, by being a space reactor we can have the pressure of the outlet be near vacuum and therefore get a much larger temperature drop. Then the Carnot limit can be above 90% and the 80% isentropic efficiency can put the thermal efficiency above 70%.
 Once you have the conversion to mechanical power the conversion then to electrical can be 95% efficient.
 Ground based power plants including nuclear ones may only get thermal conversion efficiency of ca. 30%. But this is limited by the Carnot limits of the temperatures of thermal source compared to that of the outlet, typically a cold water reservoir.
 For the nuclear powered electrical propulsion, we want to have high efficiency to avoid needing large, and heavy, radiators, to reject the waste heat. If the efficiency were only 30% or below, most of the energy produced is simply thrown away and at great mass penalty.

Can We Improve the Burn Lifetime of Space Nuclear Reactors?
 Space nuclear reactors have full-power lifetimes of just a few hours. This is compared to the fuel burn time of a few years for ground-based nuclear reactors before they need to be refueled. This is due to high temperature and high power level for their size for the space reactors. Indeed the temperature might be 3 times as high at full power for the space reactors compared to the ground ones.
 Most disconcerting is the very small amount of nuclear fuel that actually gets burned because of the short runtime for the space reactors. From that passage in "A One-year, Short-Stay Crewed Mars Mission" cited above, only 0.2% of the nuclear fuel may get burned during the engine lifetime.
 Compare this to the burn-up in ground-based reactors that might be in the range of 6.5%:

The Nuclear Fuel Cycle.

https://web.archive.org/web/20170824054559/http://www.world-nuclear.org/information-library/nuclear-fuel-cycle/introduction/nuclear-fuel-cycle-overview.aspx

 The reason why only a small portion of the nuclear fuel gets burned in any fission reactor is because the fission products after awhile build-up and inhibit the fission process. And the higher the power the reactors are run at for their size, the faster is the build-up of these fission products.
 Then a proposal that might lengthen the lifetime of the space reactors is not to burn the fuel all at once but burn it in layers, outside in. If the layers are thin enough, we should get little blockage from the fission products. Once an outer layer fuel got consumed, we would remove that layer and allow the next layer in to react.
 If we could get most of the fuel to be consumed, then we would need much less radioactive material to be sent to space so nuclear space propulsion would be much less controversial.
 This method might also work for the ground based reactors. If the ground based reactors could use most of the fuel, much less uranium would be needed to operate a reactor and you would have lower operation costs and radioactive waste being produced.


  Bob Clark

Nuclear powered VASIMR and plasma propulsion doable now.

Copyright 2015 Robert Clark

 By now all Mars advocates have heard the argument that VASIMR's 39 days to Mars promise is illusory because the needed space nuclear power sources do not exist at the needed lightweight, ca. 1,000 watts per kilo.

 This led me to propose using concentrated solar power for VASIMR or Hall effect thrusters instead:

Short travel times to Mars now possible through plasma propulsion.

http://exoscientist.blogspot.com/2014/03/short-travel-times-to-mars-now-possible.html

 I was therefore startled to read when looking at the specs of space nuclear engines that the engines themselves actually put out orders (plural) of magnitude higher power than this. See for example the specs on the "bimodal" nuclear rocket here:

Bimodal NTR.

Engine (Thrust Mode)
Thrust per engine  67,000 N
Total Thrust  200,000 N
T/W_engine  3.06
Exhaust Velocity  9,370 m/s
Specific Impulse  955 s
Propellant
Mass Flow  7.24 kg/s
Full Power
Engine Lifetime  4.5 hours
Reactor Power  335 MW_thermal
http://www.projectrho.com/public_html/rocket/realdesigns.php#id--Bimodal_NTR

 At a thrust of 67,000 N and T/W of 3.06, this means the engine weighs, 21,900 N, or 2,230 kg. So at a 335 MWthermal power this is a 150,000 watts per kg power to weight ratio. And the conversion of this thermal to kinetic energy is over 90% efficient as measured by the engine exhaust velocity.

 This means the problem with getting electrical power out of the space nuclear reactors has nothing to do with the nuclear reactors themselves. The problem is with the conversion to electrical power, specifically, the conversion/generation equipment is too heavy.

 In that vein note then there are electric motors, i.e, electric-to-mechanical conversion, with the necessary lightweight:

Power-to-weight ratio.
2.1.2 Electric motors/Electromotive generators.

https://en.wikipedia.org/wiki/Power-to-weight_ratio#Electric_motors.2FElectromotive_generators

 It turns out that electrical-to-mechanical energy conversion and vice versa is very efficient, typically in the 90% range and above. So you would run these electric motors in reverse to generate the electric power. Note then the best in that list is at 10,000 watts per kilo, sufficient for the VASIMR, and other plasma propulsion methods.

 It is important to recognize that the low electrical specific power, i.e., electrical power per weight, for space nuclear reactors is not due to the reactors themselves but due to the electrical conversion equipment. Then the focus is put on improving the electrical power generation weight efficiency. But this has importance beyond just space power systems. For instance the defense department wants lightweight electrical systems to power their UAV's. And aircraft manufacturers are investigating electrically powered aircraft for low-noise and zero-pollution aircraft. For instance LaunchPoint has produced high power density motors for UAV's in the 8200 w/kg range, which they say can be scaled up to large aircraft.

 Another area of research for high specific power motors and generators is operating them at cryogenic temperatures. According to this report 10 times as much power can be put through the windings of a motor at liquid nitrogen temperatures than at room temperature:

HIGH SPECIFIC POWER MOTORS IN LN₂ AND LH₂.
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070028414.pdf

 Then using the electric motors already getting ca. 10,000 watts/kg, we could conceivably get ca. 100,000 watts/kg by running them at cryogenic temperatures(!) This has great relevance to the space propulsion application since we could use liquid hydrogen or other cryogenics as the fuel that would also serve to keep the electric generator at cryogenic temperatures.


 However, in an upcoming blog post I'll show you don't need to do the conversion to electricity and run a plasma engine. You can get the high speeds from the nuclear engines themselves, with some minor modifications.


  Bob Clark

Short travel times to Mars now possible through plasma propulsion.

Copyright 2014 Robert Clark

 Robert Zubrin wrote a critique of the plasma propulsion system VASIMR here:

The VASIMR Hoax
By Robert Zubrin | Jul. 13, 2011
http://www.spacenews.com/article/vasimr-hoax

 The primary criticism is that it would require unrealistically lightweight nuclear propulsion. However, Zubrin doesn't even like the idea of fast propulsion to allow short travel times to Mars. He argues in favor of using 6 month or more one-way travel times to allow free return trajectories at Mars. But the health disadvantages of long travel times such as radiation exposure, bone and muscle loss, and the recently found eye damage and vision loss suggest we should investigate such short travel times.

 Now we find there is also another reason: mechanical breakdowns on such missions of 2 or more years round trip length, such as found with the coolant system on the ISS.

 Note that the argument about free return trajectories does not hold with respect to planets with atmospheres. The Apollo missions did do a free return around the Moon, but there was no non-propulsive method to slow down at the Moon. On return to the Earth though, even Apollo had a trajectory that would send it off into space if the angle was too shallow or plunging too steeply into the Earth's atmosphere to burn up if the angle was too steep. The same could be used in addition to the propulsive method whose high efficiency would also allow it to be used for slow down at Mars.

 So it is important to note we may have a short term power source instead of nuclear power, for plasma propulsion such as Vasimr at the needed lightweight.

 The key point is that the power source does not need to be nuclear. According to Zubrin's article on the Vasimr it requires a power source of 1,000 watts per kg power density. This is 100 times better than what has been done with nuclear space power at 10 watts per kg. However, it is only 10 times better than standard solar space cells at 100 watts per kg. Actually more recent space solar cells get 200 watts per kg, so it is only needs to be 5 times better than those.

Now the key fact is that solar cells can put out more power if they have more concentrated light shone on them. Estimates of how much power solar cellls put out are based on the solar insolation at the Earth's distance from the Sun. But if that light is concentrated they can put out more power. In fact some Earth solar power systems get more power by using inexpensive mirrors or lenses to concentrate light over a larger area rather than using expensive solar cells over that larger area.

A disadvantage is this increases the loss due to heat and also if the light is too intense it can overload the solar cells so they don't work at all. However a recent report claims they can use concentrated light at thousands of times higher than solar insolation:

SEPTEMBER 07, 2013
Stacked Solar Cells Can Handle Energy of 70,000 Suns.

This work is important because photovoltaic energy companies are interested in using lenses to concentrate solar energy, from one sun (no lens) to 4,000 suns or more. But if the solar energy is significantly intensified – to 700 suns or more – the connecting junctions used in existing stacked cells begin losing voltage. And the more intense the solar energy, the more voltage those junctions lose – thereby reducing the conversion efficiency.

http://nextbigfuture.com/2013/09/stacked-solar-cells-can-handle-energy.html

Several reports in fact claim solar concentration at hundreds to thousands of Suns:

FEBRUARY 20, 2009
Breakthrough Solar Concentrator:low cost with high efficiency.
http://nextbigfuture.com/2009/02/breakthrough-solar-concentratorlow-cost.html

FEBRUARY 17, 2011
Concentrated solar power at half the cost of thin film solar.
http://nextbigfuture.com/2011/02/concentrated-solar-power-at-half-cost.html

DECEMBER 16, 2011
Tiny Solar Cell Could Make a Big Difference
http://nextbigfuture.com/2011/12/tiny-solar-cell-could-make-big.html

This will be dependent on having lightweight mirrors or lenses. However another key fact is that the parabolic mirrors do not have to be telescope grade accuracy. Indeed you can find on the net videos of amateurs making their own homemade solar furnaces that also require light to be concentrated to high intensity. These homemade mirrors can be as simple as aluminum foil spread onto a cardboard frame and still concentrate light to generate thousands of degrees. Not requiring high accuracy for the mirrors suggest they can be made lightweight.

DARPA is also funding lightweight space lenses:

DECEMBER 08, 2013
DARPA shoots for 20 meter folding space telescope.
http://nextbigfuture.com/2013/12/darpa-shoots-for-20-meter-folding-space.html

 Another example of how lightweight we could make the mirrors is actually to be tested in space:

Gossamer sail set to deorbit satellites.
By Jenny Winder | 30 December 2013

https://web.archive.org/web/20150618232251/http://www.sen.com/news/gossamer-sail-set-to-deorbit-satellites

 This solar sail has 25 square meters at only 2 kg weight. Let's suppose we only need 10 times solar concentration. This should already be within the capacity of currently used solar cells to accommodate since recent research is in the 100's to 1,000's of Suns range.
At 10 times solar concentration this means the solar cells have 2.5 square meters area in order for the mirror reflecting area to be 10 times greater. If they were 100% efficient this would be 2500 watts of power under standard solar illumination, i.e., without concentration. Solar cells though typically are only in the range of 30% efficient. So they would give 750 watts under standard solar illumination. At a 200 watts per kg power density now reached for space solar cells they would weigh 3.75 kg.
Now we are assuming the sail concentrates 10 times greater surface area onto the cells, so under this concentrated illumination they will put out 7,500 watts. The total weight of the cells and sail would be 5.75 kg. And the power to weight efficiency would be 1,300 watts per kg, sufficient for the Vasimr.

 The question though is would extra mass be needed to dispense the extra heat. Low power concentrators don't need these cooling systems:

Concentrated photovoltaics.
Low concentration PV (LCPV)

Low concentration PV are systems with a solar concentration of 2-100 suns.[5] For economic reasons, conventional or modified silicon solar cells are typically used, and, at these concentrations, the heat flux is low enough that the cells do not need to be actively cooled. The laws of optics dictate that a solar collector with a low concentration ratio can have a high acceptance angle and thus in some instances does not require active solar tracking.

http://en.wikipedia.org/wiki/Concentrated_photovoltaics#Low_concentration_PV_.28LCPV.29

 We only need about about 5 times concentration with currently available space solar cells without significant loss of efficiency from the solar cells to get the needed specific power.

 For simplicity and to maintain the light weight we might want to use these low power concentrators. However, there might be lightweight, passive cooling systems that could be used for the high power concentrators, that can reach hundreds to thousands of Suns, that with the higher degree of concentration would still have a light weight at high power.

These methods would concentrate sunlight onto solar cells. However, solar cells are typically low efficiency, in the range of 30%. Another advantage of concentrators is that increase the efficiency. The latest ones can get 44.7% efficiency and researchers believe they can reach above 50%.

 Another method would eliminate the need for solar cells. That is to use a solar furnace. These can get temperatures as hot as the surface of the Sun by concentrating sunlight. By thermodynamics very high temperatures correspond to high efficiency conversion of heat to other forms of energy, 90% and above.

 An additional problem with plasma thrusters though is the high weight compared to the thrust they put out. For VASIMR the thrust to weight ratio can be calculated to be in the range of only 1 to 4,000. See for example this report for the mass of the thruster per given power on p. 2  and the thrust per power on p. 3:

Low Thrust Trajectory Analysis (A Survey of Missions using VASIMR® for Flexible Space Exploration - Part 2).
http://www.adastrarocket.com/VASIMR_for_flexible_space_exploration-2012.pdf

 Other plasma thrusters however, such as the Hall effect thruster have better thrust weight ratios, ca. 1 to 200. A recent advance may even improve on that. This report discusses "nested channel" Hall effect thrusters, which have been shown to achieve the same thrust at a lower weight:

Developmental Status of a 100-kW Class
Laboratory Nested channel Hall Thruster.
IEPC-2011-246
Table 1, Example of concentrically NHT specific mass and footprint savings, p. 5.

http://pepl.engin.umich.edu/pdf/IEPC-2011-246.pdf

 The three-channel thruster in this table only weighs 320 kg. There is an inverse relationship between Isp and thrust as shown in the graph in Fig. 3 of this report on p. 3. So for the high of 5,000 s Isp in this table, the thrust would be 36 N. Still this is a 1 to 90 thrust to weight ratio, quite good for plasma propulsion. In comparison, at a 1 to 4,000 thrust to weight ratio, the VASIMR thruster would weigh nearly 15,000 kg.

 In addition to the thruster though plasma propulsion systems need a power procession unit (PPU). This transforms the low voltage put out by solar cells, usually just a few volts, to the hundreds of volts needed for plasma propulsion. The PPU mass is often comparable to that of the thruster itself.

 However, there may be methods to reduce or eliminate this extra mass. One method might be to put the solar cells in series like with batteries to build up the voltage. There is the question though if the solar cells can handle this higher voltage. Another possibility might be to use the recent advances in nanotechnology to produce a lightweight PPU. For instance quantum dots can transform low frequency light to high frequency light. It might possible to adapt this method to transform low voltage to high voltage.

 An exciting upcoming development is the Sunjammer solar sail scheduled for launch in January, 2015:

Solar Sail Demonstrator.

http://www.nasa.gov/mission_pages/tdm/solarsail/solarsail_overview.html#.UyWr7IUcbOw

 
 This sail will have an area of 1,200 sq. m. at only a 50 kg weight. At perihelion, the solar irradiance is about 1,400 watts per square meter. This would give a maximum possible power of close to 1.7 megawatts at 100% efficiency. If using the new 44.7% efficiency solar concentrator cells, this would be 750 kwatts.

 Then as early as next year we can test high power plasma propulsion systems that can make manned missions to Mars at travels times of weeks rather than months.

  Bob Clark

UPDATE, September 1, 2015:

 The use of solar concentrators to reduce the mass of solar power systems would have applications also to space solar power. Then it is notable that a recent development in carbon nanotubes may make the required mirrors 1,000 times lighter than even the Sunjammer solar sail:

Economical Space Solar Power Now Possible.
http://exoscientist.blogspot.com/2014/04/economical-space-solar-power-now_19.html