).The concept consists of two layers of plasma sandwiched together. The outer layer is a Glow-Discharge "Cold Plasma". In this type of plasma, the Ions are relatively stationary, and the electrons do most of the moving. The energy-density of such as plasma is very low, and by connection the temperature of the plasma is essentially ambient. I've generated this kind of plasma a number of times via an apparatus consisting of a ionization-frequency glow discharge through a low density gas. The second and innermost layer is a type of plasma described as "Non-Equilibrium"-- More ions are in a heightened energy state than are in the base (ionization-frequency) state. This type of plasma is "metastable", meaning that it can jump down into a lower energy state through the emission of electromagnetic radiation. The short and sweet of it is that the outer plasma layer releases energy in a form that triggers a discharge in the second plasma if penetrated by a projectile. This energy is then directed (via the first layer) onto the projectile, either reflecting or destroying it.
This type of shielding would behave in very much the same way as a Starsiege shield. The shielding would be projected in a skin encompassing the vehicle, and might be more concisely dubbed "Plasma Discharge Armor", but for simplicity we'll stick with just 'Shields'. The shield generator for such an apparatus would consist of capacitor and oscillator components, as well as helicon-type plasma source coils. The outer layer could be projected by guiding a stream of glow-discharge plasma down a phased magnetic potential system, kind of like a magnetic conveyer belt. Upon reaching the exterior of the vehicle, a simple projection system would distribute the plasma onto the surface. [See below]
As some might remember, one variable of SS shields was "Protection Factor", the maximum amount of energy the shield can absorb. This is simply a measure of the inner plasma layer's energy. More internal energy, more possible "Shrug". The second was "Charge Factor", which is also relatively easily explained as the rate at which the inner plasma layer is photon-pumped back into it's metastable state. The last was efficiency, which is simply exactly that-- the amount of energy into the plasma layer compared to the energy required to project it. The SMOD is simply an energy manifold for the shield generator, redistributing plasma flow to different emitters. A SCAP functions as a reservoir for plasma already in a metastable state, and can be shunted into the shield directly. Its failure possibility is possibility that the metastable plasma might jump down an energy state inside the conveyer system, hence damaging it. And now for the fun stuff!
Subscripts will be denoted in { } , superscripts (exponents) will be in [ ]
Development of Energy-Based Defensive Technologies
Devlin Baker (Bakerd5@cc.wwu.edu)
December 27, 2004
Popular Science Fiction is full of references to "Energy Shields"; Energy based systems for protection from weapons fire. This paper will investigate the plausibility of such a technology, and develop a possible concept for a functional system. We will for the most part consider protection only from projectile weapons, though laser and energy-based weaponry will be addressed in the final section.
Section 1: Conventional Armor
Approaching the problem of energy shielding it is helpful to first investigate how conventional armor functions. A projectile of mass m and traveling at a velocity v will impact armor with a kinetic energy, K, of:
K = (½ mv[2] ) Sin è
Where è is the angle between the surface of the armor and the projectile's path. In general there are two types of projectile impact: Shrug and absorption. Absorption occurs when structural elements of the armor break down upon impact, leaving the projectile imbedded in the armor. The depth of the projectile's penetration into the armor (Distance from the surface to the point of v = 0) will be denoted L{P} throughout this paper. When a projectile is shrugged, it is reflected away from the surface of the armor, with a minimal amount of structural damage to the material composing the armor. This requires a degree of elasticity of the armor, as the surface bends inward a certain distance (dependent on a number of factors, including the tensile strength of the material, the energy delivered by the projectile, etc). The distance the armor rebounds will be designated L{R}. For an impact of a projectile with cross sectional area A, the work done on the projectile is;
W = ΔK = ((½ mv[2] ) Sin θ ) = (F{app} )(L{P})
Where F{app} is the force applied over area A. Therefore;
F{app} = ((½ mv[2] ) Sin θ )/(L{P})
F{app} = FA
F = ((½ mv[2] ) Sin θ )/(L{P}A)
Hence F is the force per unit area on the armor. Here some obvious optimizations for armor become clear. To reduce the force per unit area, Both A and LP should be large. A can be increased by spreading the force over a larger area, which can be accomplished by placing rigid structure within the armor. L{P} is effectively the thickness of the armor for an absorbed impact, or L{R} if the impact is shrugged. Therefore very thick armor or highly elastic armor is optimal. For material armor, these quantities are limited by metallurgical processes and mass, as multiple meters of steel are not always practical. However, advances in metallurgical processes allow for the use of materials, such as depleted uranium (U238), with very high densities. This increases the molecular inertia of the material, allowing it to absorb greater force per unit area without loss of structural integrity.
Section 2: Energetic Armor
Current "exotic" armor technologies, such as reactive armor can be considered "Energetic Armor". These technologies contain stored energy (usually in chemical form) that is released to neutralize a projectile. Reactive armor consists of boxes attached to the exterior of the vehicle. Each box contains an explosive charge sandwiched between steel plates. Impervious to small arms fire and shrapnel, the charge detonates on contact with a shaped charge warhead. The explosion blows the plates apart disrupting the warheads plasma jet, rendering the round ineffective. Reactive armor can increase the effectiveness of conventional armor up to 5 times but it has its drawbacks. Once a panel blows it leaves that spot vulnerable to future attacks and it is not effective against kinetic rounds. Now being developed are so-called "Charged Armor" systems. These technologies charge the armored hull of the vehicle via a massive capacitor, resulting in substantial energy release upon projectile impact. While these systems may prove more practical against shaped charges, they are still not effective against kinetic rounds.
Section 3: The Effect of a Projectile on 'Cold Plasma'
In an ideal Cold Plasma, equal numbers of electrons (electrical charge –e) and ions (electrical charge e) are motionless, and homogeneously distributed. Initially we will consider only the ions and their dynamics. We will assume that the mass of the ions and incident projectile are far greater than that of the electrons, and that their inertial contribution is dominant. As such, the inertia of the ions keeps them motionless on the time scale of interest. The initial charge density is zero everywhere, due to the uniform distribution of the electrons and ions. If the plasma is then perturbed by some force, say by a projectile, and all of the ions in a specific locality are shifted, a local region of positive charge results. Here we will assume that only the ions are affected by the initial perturbation. An adjoining region of negative charge that is depleted of ions results; beyond this region, the rest of the plasma is neutral. The charge separation created by perturbing the ions is the source of an electric field, and, at the same time, this electric field will act on the electrons and ions, consistent with Poisson's equation. The electric field then accelerates the electrons back to their initial positions, so that momentarily the charge density is everywhere zero, resulting in zero electric field. At this point, however, the electrostatic potential energy consequential of the original perturbation has been transformed into kinetic energy of moving electrons (The ions as well, but massing many factors of 10 more, their velocity is negligible). This kinetic energy is sufficient to carry the electrons past their initial positions. As they move away, they leave behind a region of net positive charge. This results in an electric field, opposite in direction to the initial perturbation's field, which retards the electrons and eventually brings them to a stop. Here their kinetic energy has been converted back into electrostatic potential energy, reversing the initial configuration. This is the first half-cycle of an electron plasma oscillation, which can be generalized as a form of simple harmonic motion. At any point the electrons are out of their initial positions, a restoring force F{R} results,
F{R} = -kx
Where x is the parallel displacement of the electron from its initial position and k is analog to a spring constant; being the force per meter of displacement. k is a relation of the electric field that results from displacement.. Similarly, the energy stored in this plasma oscillation is simply E = kA[2], with A being the amplitude of the oscillation. Making the maximum velocity of the electron;
v{max} = A√(k/m{e})
The velocity of the electron at any point of the oscillation is therefore-
v = A√(k/m{e}) √[1- (x[2] / A[2] )]
Using equation 3.2, a generalized expression for k can be found:
k = √(2m{e}E/v[2]) = [(2m{e}E[2])/A[2] ]1/3 = √(m{e}E) / 16
Resulting in the somewhat surprising relation that k is dependent only on the mass of the electron and the stored energy. The maximum velocity can then be found as a function of the stored energy,
v{max} = A√(k/m{e}) = A√((√(m{e}E) / 16))/m) = A (E[1/4] / (256me[1/4]))
Thus the maximum velocity is a function of the stored energy and the amplitude of the oscillation, which is dependent on the density of the plasma. It is worth note that because v{max} = ωA , the electron plasma frequency ω{pe} is:
ω{pe} = (E[1/4] / (256m{e}[1/4]))
Therefore;
a{max} = ω{pe}[2]A = (E[1/2] / (256me[1/4] )[2])A
This harmonic motion could in principle continue indefinitely, as the perturbed electrons move back and forth past their equilibrium position, converting electrostatic energy into kinetic energy and back again. However, since an accelerating charge radiates energy in the form of electromagnetic waves, it looses energy at the rate
dE/dt = ae[2] /(6πε{0}m{e}c[3])
This shows that the electron plasma oscillation is best described as damped harmonic motion, being subject to the equation
x = Ae [–(b/2m)t] cos(√( (k/m)-(b[2] /4m[2] ))t)
Where t is the time elapsed since the initial perturbation and b is similar to k, in that it is the proportionality constant of the radiative dampening effect. The "dampening force", always acting opposite to the electron's velocity vector, has magnitude F{damping} = -bv ; v being velocity. Because the loss of energy dE/dt will exert Fdamping over the amplitude A, we find b to be equal to:
b = - ((E[1/2] / (256m{e}[1/4] )[2]) e[2] )/ 6πε{0}m{e}c[3]A[2]√(k/m{e}) √(1- (x[2] / A[2])))
b = - (ae[2] / 6πε{0}m{e}c[3]Av)
This clearly shows that the amplitude of the first cycle of the electron plasma oscillation will be the greatest. It follows, then, that the radiation emitted from the oscillation will have the greatest frequency directly following the perturbation. Assuming cyclic emission of radiation (one quanta per half-period of oscillation), the frequency of the emitted radiation will be:
ω = E{Δ}/h
Where E{Δ} is the energy difference between the initial and final energy state of the electron plasma oscillation, and h is Planck's constant. E{Δ} can be determined using equation 3.10, as E{Δ} is equivalent to the work done on the electron by radiative forces, equal to W= –bvA. Therefore,
E{Δ} = –bvA
E{Δ} = –(ae[2] / 6πε{0}m{e}c[3]Av)vA
E{Δ} = –(ae[2] / 6πε{0}m{e}c[3] )
Here a is the acceleration, or dv/dt of the system, which is equal to -A(E1/4 / (256me1/4)), making:
E{Δ} = ((A(E[1/4] / (256me[1/4]))) e[2] / 6πε{0}m{e}c[3] )
ω= ((A(E[1/4] / (256m{e}[1/4]))) e[2] / 6πε{0}m{e}c[3] ) / h
Equation 3.13 therefore gives the frequency of emitted radiation for a transfer of energy E into plasma with electron plasma oscillation amplitude A. As this radiative damping continues, the frequency of emitted radiation will decrease at a rate proportional to a. In the case that the transfer of energy was kinetic from an incident projectile, it is clear that the plasma would have the effect of slowing the projectile by "Bleeding away" its kinetic energy. However, it is likely that for any real-world projectile velocity, the density of the plasma would have to be extreme to have much effect before the projectile passed completely through the plasma. However it may be possible to multiply the "Kinetic Bleeding" effect, which will be investigated in the next section.
Section 4: Stimulated Emission in Non-Equilibrium Plasmas
Stimulated emission is possible in plasmas where there is a population inversion, a non-equilibrium condition where more quantum systems are in the higher excited state than the lower state of a particular transition. Rapidly cooled plasma can produce a population imbalance in which there are more ions in an upper energy level than in the lower. Of course, this "Cooling" need not necessarily be thermal; a bleeding mechanism similar to that described in the previous section may function just as well. The plasma will inevitably "jump down" into a lower energy state, either triggered by an outside force or spontaneously. Spontaneous emission can be considered a stimulated emission reaction, but induced by virtual photons from the Quantum-Electrodynamic vacuum fluctuations that compose the zero-point field. However, if triggered by an (externally produced) incident photon, an ion in the plasma can make a transition to the lower energy state, creating another photon in the process. To satisfy conservation of energy, the energy difference between the upper and lower states exactly matches the photon energy, so the frequency of emitted radiation is identical to the incident. This can also be explained in that the temporal evolution of the coherent superposition of the lower and upper quantum wave functions act much like an oscillating dipole antenna; emitting electromagnetic radiation. The emitted photon then continues to propagate at velocity c, leaving the de-excited ion in its lower energy state. The alternating electric field creates a dynamic stark effect perturbation which increases the transition probability, making an encounter with another atom probable. Due to this and the relatively high density of the plasma, the photon will encounter another excited ion of the same species and stimulate a transition identical to that which formed it. The probability of this transition depends on the strength of the electric field produced by the emitted photons, and is directly proportional to the number of photons already present in the environment—Meaning that more times such an encounter takes place, the more likely it is to again. This second transition creates a second photon with exactly identical properties to the emitted photon as well as the incident photon. The two photons are identical; they have the same phase and wavelength. They form a Bose-Einstein condensate where all the constituent photons contribute to create a macroscopic quantum state, whose amplitude is much greater than the random spontaneous emissions occurring in ordinary plasma—and also identical to the initial incident photon. This "Photon Chain Reaction" increases exponentially per unit distance, eventually resulting in a quantum-coherent release of electromagnetic radiation exponentially more energetic than the initial incident photon, but exactly in phase and of matching frequency. This is, incidentally, an exact analog to the working principle of a laser. Per work done by Einstein, it is known that on thermodynamic grounds the probability for spontaneous emission, α, is related to the probability of stimulated emission, β, by the relationship:
α /β = 8πhω3/c3
From the development of the theory behind blackbody radiation, it is known that the equilibrium radiation energy density per unit volume per unit frequency was equal must be equal to this ratio α : β. As one would expect, the probability of spontaneous emission is greater if the energy density of the plasma is greater. This makes the energetic state more unstable, and limiter mechanisms of some sort would be required to prevent a random discharge of the plasma's energy.
Section 5: Prospects for Energetic Shielding
(FIGURE 5.1)
The concept presented in figure 5.1 may be a workable model for energetic shielding. It consists of two layers of plasma, of depth l1 and l2 , separated by a distance d and backed by a mirrored surface. The outer layer is a Glow-Discharge "Cold Plasma", like that described in Section 3, of ion density ρ1. The inner layer is Non-Equilibrium plasma with ion density ρ2 and an inverted ion energy population, like that described in Section 4.
If an incident projectile with mass m, velocity v, and cross-sectional area A impacts the cold plasma layer at a right angle, the energy of the projectile is:
K = ((½ mv[2] ) Sin (π/2)
K = ½ mv[2]
Therefore the applied kinetic energy per unit area is K/A,
E{app} = (½ mv[2] ) / A
Considering at period of time t after the projectile makes contact with the surface of the plasma, the distance penetrated into the plasma layer will be simply vt. We will consider only times for which vt < l1. The number of perturbed electrons will therefore be the volume of projectile penetration multiplied by the ion density, ρ1—
n{e} = vtAρ1
Hence the energy applied to each ion will be;
E{ion} = K / n{e} = K / vtAρ1
E{ion} = (mv) / (2tAρ1)
Where m is the mass of the projectile. In the process described in Section 3, this energy is transferred to the far less massive electrons, inducing electron plasma oscillations of frequency,
ω{pe} = (E{ion}[1/4] / (256m{e}[1/4]))
ω{pe} = (mv[1/4] / ((256m{e}[1/4])( 2tAρ1) [1/4]))
The period of these oscillations is then simply 2π /ω, which will radiate energy at a rate of;
dE/dt = ω{pe}[2]Ae[2] /(6πε{0}m{e}c[3])
dE/dt = mv[1/2]Ae[2] / ((6πε{0}m{e}c[3])((256m{e}[1/4])( 2tAρ1) [1/4]))
Just as before, the frequency of emitted radiation is then::
f= ((A(E[1/4] / (256m{e}[1/4]))) e[2] / 6πε{0}m{e}c[3] ) / h
f= ((A((mv) / (2tAρ1)[1/4] / (256m{e}[1/4]))) e[2] / 6πε{0}m{e}c[3] ) / h
Therefore n photons with energy hf will propagate outward from the cold plasma. This will cause a "Photon Chain Reaction" in the second layer of plasma, as discussed in Section 4. Such a reaction increases exponentially per unit distance, eventually resulting in a quantum-coherent release of electromagnetic radiation exponentially more energetic than the initial incident photon, but exactly in phase and of matching frequency. If the photons emitted from the cold plasma arrive over cross-sectional area a and the initial probability of stimulated emission is S, there will be n{react} reactions—
n{react} = n{p}aTS
T is the opacity of the plasma. If the rate of reaction probability increase is s(x), the total number of photons emitted over the depth of the plasma l2 is-
n{photon} = (n{react} ) s(x)l
n{photon} = (n{p}aTS ) s(x)l
Having now traveled the entire depth of the plasma, distance x is now simply l2. The total energy exiting the plasma is then--
E{incident} = n{photon} (hf)
E{incident} = (npaTS ) s(x)l (hf)
E{incident} = (npaTS ) s(x)l ((A((mv) / (2tAρ1)[1/4] / (256m{e}[1/4]))) e2 / 6πε{0}m{e}c[3] )
These photons will be reflected off the mirrored surface and travel back through the second section of plasma. This will of course cause a second round of stimulated emission reactions, however this can be accounted for by changing l2 to 2(l2).
This discharge of coherent photons will reach the incident projectile after time t = 2(d + l2 ) / c. The projectile will have traveled distance 2v(d + l2 ) / c. The energy lost to the plasma will be equal to-
E{lost}= (4π(d + l2 ) / cω) n
E{los}t= (4π(d + l2 ) / cω) ((A((mv) / (2tAρ1)[1/4] / (256m{e}[1/4]))) e[2] / 6πε{0}m{e}c[3] )
Where n denotes the number of complete oscillations the electron plasma will have gone through since the initial impact. The energy Eincident results in a massive radiative force on the plasma and contained projectile. The total energy of the plasma contained within the parallel bounds of emission region a now becomes:
E{final} = E{app} - E{lost} + E{incident}
E{final} = ((½ mv[2] ) + (npaTS ) s(x)l ((A((mv) / (2tAρ1)[1/4] )/ (256m{e}[1/4]))) e[2] - (4π(d + l2 ) / cω) ((A((mv) / (2tAρ1)[1/4] / (256m{e}[1/4]))) e[2] / 6πε{0}m{e}c[3] )
However, because the base energy of the plasma was defined as E = 0, the plasma must somehow loose this energy to return to its base energy state. This will be in the form of electromagnetic radiation emitted from the plasma. The great majority of this radiation will me emitted along the vector –v'', parallel to the initial projectile's path but opposite in direction. The radiation pressure on the projectile can be determined using a pointing vector relation, for cross-sectional area of the projectile a,
S = (1/a)(dU/dt) = ε{0} cE[2]
P= ((R + 1) ε{0} cE[2] ) / c
Where R is the reflectivity of the projectile. Here E will be the energy delivered to the projectile, equal to the portion of the radiative discharge that is directed in the –v'' direction. This is, incidentally, simply the value Eincident, as this radiation is already coherent and directed in the correct direction. Elost will contribute a small amount to the final energy, but this will be ignored due to its infinitesimal magnitude for simplicity. The energy Ereturn, the energy imparted on the projectile opposite to its kinetic energy vector, is therefore Eincident. Hence the radiation pressure has magnitude-
P= ((R + 1) ε{0} c E{incident} [2] ) / c
P= ((R + 1) ε{0} c ((npaTS ) s(x)l ((A((mv) / (2tAρ1)[1/4] / (256m{e}[1/4]))) e[2] / 6πε{0}m{e}c[3] ))[2] ) / c
Because P= F/a, the force on the projectile is:
F{return} = ((R + 1) ε{0} c E{incident}[2] )a / c
A quick check on the ratio of F{return} and F{app} shows that F{return} > F{app}. Quite simply, this will impart an acceleration on the projectile,
Acceleration = ((R + 1) ε{0} c E{incident}[2] )a / m{p}c
With m{p} being the mass of the projectile. The direction of acceleration will again be opposite to the projectile's initial kinetic vector. Because F{return} > F{app} , the projectile will be either stopped or reflected.
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Damn that hurt.
To those of you that are diehard that shields are "Modulated Electromagnetic Fields", I've produced this: A model of that described above, using only EM fields. Hooray.
