[SIZE=+2]Thermonuclear Fusion Propulsion
[SIZE=+1]Introduction
The use of thermonuclear fusion for propulsion has the potential to open up the entire solar system for human exploration. Only fusion provides the high efficiencies needed by interplanetary spaceships to prevent fuel requirements from becoming overwhelming. Chemical rocket engines using liquid hydrogen and liquid oxygen work well for operation in the near earth environment including the moon, however, they are totally inadequate for interplanetary voyages. This inadequacy is due to the fact that there is only so much energy which can be extracted per pound of fuel, and it is this limitation which puts restrictions on the maximum efficiencies attainable. Rocket engine efficiency is expressed in terms of a quantity called specific impulse or Isp and is measured in seconds. Physically, specific impulse is the number of seconds a rocket engine can produce one pound of thrust from one pound of fuel. It is analogous to miles per gallon for an automobile. In general, specific impulse increases with increasing propellant exhaust temperature. Based on thermodynamic analyses (see Appendix A) with 100% efficient operation in space (i.e. vacuum), specific impulse may be calculated using the following equation:
where:
Isp = Specific Impulse (sec lbf/lbm)gc= Conversion factor (32.2 lbmft/lbf/sec2)g = Specific heat ratio of exhaust gas (typically 1.4)M.W. = Molecular Weight of exhaust gas Ru= Universal Gas Constant (1545.4 ft lbf/lb-mole/R)Te= Temperature of exhaust gas (R = F + 460)
Since chemical rocket engines using liquid oxygen and liquid hydrogen typically operate at exhaust temperatures of about 6000 F (3600 K) under stoichiometric conditions yielding effective molecular weights of approximately 11, we find the specific impulse of these engines is limited to about 450 sec.
Nuclear rocket engines using fission reactors to transfer heat to hydrogen propellant perform somewhat better than chemical engines having specific impulses of about 960 sec. This advantage, however, is due mainly to reductions in the effective molecular weight of the exhaust gas (2 vs 11) rather than increases in exhaust temperature. In fact, nuclear rockets are expected to operate at lower exhaust temperatures than chemical rockets ( 5000 F or 3000 K) due to materials limitations of the reactor core. The vast amount of energy potentially available through the fission process remains largely untapped due to size constrains associated with the minimum critical mass required to sustain the fission chain reaction and the difficulty of efficiently extracting heat at ultra high temperatures from the reactor.
Fusion rocket engines using a reacting plasma (hot ionized gas), on the other hand, do not suffer from
the energy or materials limitations imposed on chemical or nuclear fission rockets. The hot plasma ( 180,000,000 F or 100,000,000 K) is maintained through thermonuclear reactions and is confined and directed through the use of magnetic fields. The specific impulse for this reaction is therefore about 130,000 sec assuming an effective molecular weight of 4 for the fusion products. In automotive terms this efficiency is equivalent to a car getting 7000 mpg!
[SIZE=+1]The Problem of Interplanetary Travel
The chief difficulty in achieving routine manned space flight to the various planets in the solar system is associated with the tremendous amount of energy required to provide velocity increments associated with the following primary thrusting maneuvers:
[RIGHT]1.[/RIGHT]
Acceleration of the spaceship to a velocity sufficient to escape the earth's gravitational field[RIGHT]2.[/RIGHT]
Acceleration of the spaceship sufficiently so as to traverse the distance to the destination planet in a "reasonable" amount of time.[RIGHT]3.[/RIGHT]
Deceleration of the spaceship to the extent that it may be captured into orbit around the destination planet.[RIGHT]4.[/RIGHT]
Acceleration of the spaceship to a velocity sufficient to escape the gravational field of the destination planet after the exploratory part of the mission is completed.[RIGHT]5.[/RIGHT]
Acceleration of the spaceship sufficiently so as to traverse the distance back to earth in a "reasonable" amount of time.[RIGHT]6.[/RIGHT]
Deceleration of the spaceship to the extent that it may be captured into orbit around earth at the end of the mission.
The sum of the velocity changes resulting from the above thrusting maneuvers yields a total mission velocity (Vt). This velocity can vary considerably between missions and is influenced greatly by the relative positions of the planets at the start of the mission and by the total trip time desired. The amount of fuel required to accomplish a particular mission is related to the total mission velocity and the rocket engine specific impulse through the famous rocket equation given below (see Appendix B):
where: mf = mass of fuel and ms = mass of unfueled spaceship
In the table below, the rocket equation is used to calculate the fuel requirements for several typical missions using chemical, nuclear fission, and nuclear fusion engines. Ratio of Fuel Mass to Spaceship Mass for Different Missions and Different Rocket Engines
PlanetTotal Velocity
(km/sec)Chemical
Isp = 450 secNuclear Fission
Isp = 950 secNuclear Fusion
Isp = 130,000 secMoon62.9.900.005Mars25286140.020Saturn707.65×10618200.056Pluto1805.02×10172.42×1080.152
From a practical standpoint, it is difficult to construct space vehicles in which the fuel mass is much more than about 20 times the mass of the spacecraft. With this criteria in mind, we find from the above table that chemical engines are suitable only for near earth and lunar missions, nuclear fission engines are suitable for Mars missions, and all missions are possible with nuclear fusion. Fusion engines are thus capable of performing any future mission within the solar system being contemplated by NASA.
[SIZE=+1]Fusion Processes Thermonuclear fusion is the process in which two or more isotopes of light elements come together or fuse to create new heavier elements and prodigious amounts of energy. Fusion is the process which the sun uses to produce its energy. Although there are number of fusion reactions possible, in reality only two or three are considered feasible for use in a fusion rocket engine. They are:
and
The chief difficulty facing those who would design fusion systems stems from the fact that in order for the reactions to take place, the nuclei of the reactants must be brought close enough for the strong nuclear force within the nucleus to exert sufficient attractive force to overcome the coulomb repulsive forces exerted by the positive nuclei. This is accomplished by raising the temperature of the reactants to the point where they have sufficient activation energy for the reactions to proceed. The temperatures required for fusion are truly enormous.
Reaction (1) above (the easiest of all fusion reactions to achieve) requires temperatures of approximately 100,000,000 K to achieve significant reaction rates.)
Reaction (2) (the second easiest fusion reaction to achieve) requires even higher temperatures of approximately 600,000,000 K.)
While the first reaction is the easiest to achieve in practice, it does have one significant drawback. That drawback is that most of the energy released in the reaction is in the form of high energy neutrons which are difficult to use effectively for propulsion purposes. The second reaction, while it does have a higher ignition temperature, does have the advantage that virtually all the energy released is in the form of charged particles which are much useful for propulsion applications. The reason charged particles are desired for propulsion systems is due to the fact that they can be directed into a rocket exhaust stream through the use of magnetic nozzles. Neutrons, on the other hand, are unaffected by magnetic fields and are therefore much more difficult to control. They also create radiation shielding problems.
Besides the high temperatures needed, the reactions must also meet a requirement called the Lawson Criterion. This criteria states that the reactant density times reactant confinement time must be greater than approximately 1014 sec-ion/cm3. Basically what this says is that the reactants must be kept together for a long enough time to ensure that sufficient fusion reactions take place to produce enough energy to keep the reaction going. Applying the Lawson criterion in different ways can lead to radically different methods of achieving fusion conditions. One method, called inertial fusion, relies on the use of laser beams to both heat and compress small pellets
of fusionable material to high temperatures and high densities for very short amounts of time. Inertial forces keep the pellet together for sufficiently long periods of time for the fusion reactions to take place. Another method, called magnetic fusion, confines a reacting plasma in magnetic fields for considerably longer periods of time, but at much lower densities. Plasma heating is accomplished primarily through the use of microwaves (just like in a microwave oven) and by injecting high energy reactant ions into the plasma through the use of a device called a neutral beam injector.
Fusion rocket engines theoretically can be built using either inertially based systems or magnetically based systems. Magnetically based systems would typically expel streams of plasma out magnetic nozzles to produce thrust. Because magnetic fields are used to contain the plasma, reaction (2) above is ideally suited to such systems. Inertial fusion systems, on the other hand, typically would use small, rapidly timed fusion explosions external to the spaceship to kick the vehicle forward. Inertial systems, are thus better able to use reaction (1) above since magnetic confinement of the fusion reaction is not required.
[SIZE=+1]Gas Dynamic Mirror Fusion Propulsion System
The Gasdynamic Mirror or GDM is an example of a magnetic based fusion propulsion system. Its design is particularly simple, consisting primarily of a long slender solenoid (basically a stack of ring shaped magnets) surrounding a vacuum chamber which contains the plasma. The fusing plasma is trapped within the magnetic fields of a series of toroidal shaped magnets in the central section of the device (green), while stronger end mirror magnets (blue) prevent the plasma from escaping too quickly out the ends. Figure 1 illustrates the manner in which the magnets are configured within the solenoid. Early experiments with mirror fusion machines were not terribly successful in that it was found that the plasma could not be stably confined within them. Plasmas, it seemed, had minds of their own, wriggling and twisting to escape the confining magnetic fields. In reality, there were two mechanisms at work causing the instabilities. Figure 1: Magnet Configuration of Gasdynamic Mirror Propulsion System
One reason for the instabilities had to do with excessive curvature of the magnetic field lines within the solenoid. Ideally, the plasma ions should spiral along the magnetic field lines and not jump from one line to another. When the field lines are curved in a certain way, however, centrifugal forces arise which tend to cause the plasma ions to drift across the magnetic field lines. Eventually this drift results in the plasma coming in contact with the containment wall and cooling the plasma to the extent that the fusion reactions are quenched. This type of instability is called a magnetohydrodynamic (MHD) or flute instability. To combat this instability, the Gasdynamic Mirror is constructed long and thin such that the magnetic field lines it generates are straight throughout most its length. Regions of high magnetic field curvature are restricted to small zones near the magnetic mirrors at the ends of the device. Figure 2 illustrates a cross-section of the Gasdynamic Mirror showing the shape of its internal magnetic fields.
Figure 2: Magnetic Field Lines in the Gasdynamic Mirror
Another source of instabilities in mirror fusion machines has to do with the rate and manner in which plasma ions are lost through the ends of the device. It turns out that if the plasma ions happen to be traveling within a certain limited cone of directions, they will definitely escape out the end of the device. This loss of a group of ions having a given cone of velocities sets up an instability called a loss cone microinstability and results in the device being unable to confine the plasma. This instability can be controlled by allowing a certain amount of plasma to leak past the throat (narrow part) of the mirror. Mirror machines in the past which strove for maximum confinement and which also operated at low plasma densities suffered greatly from this instability due to the fact that the ions had to travel back and forth between the mirrors many times before they underwent a collision which resulted in a fusion reaction. Instabilities at the magnetic mirrors then would thus be communicated throughout the entire length of the device, totally disrupting the plasma containment. In the Gasdynamic Mirror this instability is controlled by letting plasma leak by the throat (indeed, this leakage is necessary if the device is to produce any thrust) and by increasing the plasma density in the main body of the solenoid to the extent that ion collisions occur there frequently. This high collision frequency prevents any loss cone microinstabilities which do occur from being communicated throughout the length of the device since the instability is essentially "forgotten" after a majority of plasma ions undergo collisions after traveling a short way away from the mirrors.
Figure 3: Interplanetary Vehicle Using a Gasdynamic Mirror Fusion Propulsion System
Titan Flyby
[SIZE=+1]The Gasdynamic Mirror Fusion Experiment at Marshall Space Flight Center
The purpose of the Gasdynamic Mirror Fusion Experiment is to build a small subscale device which can be used to investigate the feasibility of the concept and in particular determine if the plasma can indeed be stably confined within the machine. A full sized device would produce thousands of megawatts of power and would be over 100 meters long. Figure 3 is a conceptual drawing of an interplanetary spaceship using the Gasdynamic Mirror as its primary propulsion system. The experiment at Marshall Space Flight Center will not be nearly so ambitious. It will be approximately 3 meters long initially, with provisions having been made to extend the length to up to 7 meters and will operate with plasmas running at temperatures far below those needed to initiate fusion. It will be able demonstrate, however, most of the operational characteristics of the full sized engine. It will also be quite flexible in that it will be constructed so that the configuration of the magnets can be changed easily to accommodate changing experimental objectives. In the future, assuming the concept continues to show promise, the device will be lengthened and the plasma temperatures raised to the point where some fusion reactions should occur. At this point, investigations will be made as to whether the plasma will remain stable when it is hot and reactive. If these experiments also prove to be successful, enough information will have been obtained to make intelligent decisions regarding the construction of a full scale fusion rocket engine to power interplanetary spaceships to voyages throughout the solar system.
[SIZE=+1]Appendix A
[SIZE=+1]Derivation of Specific Impulse
Specific Impulse is defined as thrust divided by the propellant flow rate or:
Where ue is the velocity of the rocket exhaust gas. The square of this propellant gas velocity is related directly to the enthalpy imparted to the gas through chemical, nuclear, etc. processes.
Physically, this equation relates the change in the propellant kinetic energy to the enthalpy change of the propellant. Noting that:
We find that the specific heat of the propellant gas can be expressed solely in terms of the specific heat ratio (g) and the molecular weight of the propellant gas:
If we now combine equations (1), (2), and (3) and assume that the initial temperature of the propellant is near zero (usually a good assumption for liquid hydrogen) we find that:
Where:公式
Isp = Specific ImpulseTi = initial temperature of propellantue = propellant exhaust velocityTe = exit temperature of propellant F = thrustcp = specific heat at constant pressure m.= propellant flow ratecv = specific heat at constant volumehi = initial enthalpy of propellantg = specific heat ratiohe = exit enthalpy of propellantM.W. = propellant molecular weightRu = Universal Gas Constantgc = unit conversion factorr = propellant densityA = nozzle cross-sectional area
[SIZE=+1]Appendix B
[SIZE=+1]Derivation of the "Rocket Equation"
To begin the derivation of the rocket equation we note that a rocket's time rate of change of momentum is equal to the external force applied to the rocket, or:
If there are no external forces acting on the rocket (e.g. due to gravity, air resistance, etc.) the above equation reduces to:
Physically, the first term in the above equation represents the momentum change in the rocket due to a differential change in the velocity of the rocket, and the second term in theabove equation represents the momentum change of a differential mass of propellant as it is expelled from the engine at a velocity ue relative to the rocket (since ue = gc Isp). Rearranging terms in the above equation and integrating we find that:
However, since the initial mass of the rocket is equal to the mass of the spaceship plus the mass of the fuel we find that:
Where: 公式
V = instantaneous velocity of rocketgc = unit conversion factor m = instantaneous mass of rocketmf = mass of propellantVf = final velocity of rocket Isp = Specific Impulse ms = unfueled mass of rocketue = exhaust velocity of propellant
For more information see the Gas Dynamic Mirror Fusion Propulsion Experiment作者: JUVENTUS 時間: 06-5-12 14:42 標題: 回覆: [轉] 台灣核武之謎 请问，台湾的地盘这么小，有地方进行核试验么？？！！ 海上？！作者: ViewSonic 時間: 06-5-12 15:17 標題: 回覆: [轉] 台灣核武之謎 [quote=JUVENTUS]请问，台湾的地盘这么小，有地方进行核试验么？？！！ 海上？！[/quote] 沒有啦～ 這一偏文章是說～ 台灣＠的核子武器發展史～ 但被老美阻止功敗垂成～作者: 常在我心 時間: 06-5-12 21:38 標題: 回覆: [轉] 台灣核武之謎 [quote=JUVENTUS]请问，台湾的地盘这么小，有地方进行核试验么？？！！ 海上？！[/quote]
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