NASA/CR-2000-210654 Theoretical Analysis of the Electron Spiral Toroid Concept Jean-Luc Cambier and David A. Micheletti MSE Technology Applications, Inc., Butte, Montana December 2000 NASA/CR-2000-210654 Theoretical Analysis of the Electron Spiral Toroid Concept Jean-Luc Cambier and David A. Micheletti MSE Technology Applications, Inc., Butte, Montana National Aeronautics and Space Administration Langley Research Center Hampton, Virginia 23681-2199 Prepared for Langley Research Center under Purchase Order L-8871 December 2000 Acknowledgments Work was conducted through the U.S. Department of Energy-National Energy Technology Laboratory at the Western Environmental Technology Office under DOE Contract Number DE-AC22-96EW96405. The use of trademarks or names of manufacturers in the report is for accurate reporting and does not constitute an official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics and Space Administration. Available from: NASA Center for AeroSpace Information (CASI) 7121 Standard Drive Hanover, MD 21076-1320 (301) 621-0390 National Technical Information Service (NTIS) 5285 Port Royal Road Springfield, VA 22161-2171 (703) 605-6000 Contents Section / Page Figures ... iv Tables ... iv Executive Summary ... 1 1. Introduction ... 2 2. Fundamental Dynamics ... 3 3. The EST Configuration ... 5 4. Stability Problems ... 11 5. The EPS Theoretical Model ... 14 6. Scaling Properties ... 18 7. Energy Storage and Lifetime ... 21 8. Experimental Observations ... 30 9. Conclusions ... 32 10. References ... 35 Executive Summary This report describes the analysis by MSE Technology Applications, Inc. (MSE) of the Electron Spiral Toroid (EST) concept being developed by Electron Power Systems Inc. (EPS). This analysis was conducted for the National Aeronautics and Space Administration's Langley Research Center (NASA-LaRC). The EST is described by EPS as a plasma shell of toroidal shape, in which electrons are in orbits around the toroidal axis. The current produced by the electron motion generates a toroidal magnetic field, which is confined within the torus shell. It is claimed that this plasma structure is very stable and can store vast amounts of energy, primarily as a magnetic field. The most detailed description is found in a theoretical study of the EST concept performed by the Massachusetts Institute of Technology (MIT) and published by EPS, herein listed as reference [1]. EPS also recently published the Phase I report for a NASA Institute of Advanced Concepts (NIAC) award, in which some of the specific claims about lifetime and energy density storage were made, denoted herein as reference [2]. The present analysis was originally based on these and another document describing the EST concept, which was also published by EPS [3]. However, dissemination of an early draft of this report led to a further exchange of information between MSE and EPS [4]; the release of two new documents [5,6]; and multiple revisions of the model by EPS. Reference [5] is actually a revised version of [3], and the second document [6] is an experimental report for the Defense Special Weapons Agency (DSWA). The analysis of this additional material is included in the final version of this report. Following the original description of the EST, the present analysis is mainly based on the cold-fluid equations for the plasma shell coupled to the self-generated magnetic field. The dynamical equations of the cold electron fluid, as well as the numerical solutions, are found to match those presented in [1]. However, these equations only represent an incomplete subset of the plasma dynamics, since the ion motion was ignored. It is easily seen that the ion fluid is unstable, due to the repulsing electrostatic field required for electron confinement. A detailed analysis with the numerical procedure confirmed these results. The EST concept requires an excess of positive charges, and the potential well thus created is responsible for confining the electrons as well as the magnetic field stored within the torus. Although various scenarios for ion confinement were then suggested [4,8] by EPS and MIT, none of them is plausible. In fact, it is demonstrated in this report that this problem is fundamental and cannot be solved within the context of the proposed EST configuration. Several problems were also found with the results presented in [2] regarding the physical characteristics of a high-energy EST, which were found to be inconsistent with the scaling properties of the numerical solutions. The rates of energy losses through collisions and cyclotron emission were also examined and found to be in error by several orders of magnitude. Furthermore, the analysis by EPS of the experimental data [6] does not provide proof of an EST, as defined in [1]. It is demonstrated in this report that the claims of absolute stability and large energy storage capacities of the EST concept have not been substantiated. However, there is undeniable experimental evidence of some type of plasma structures whose properties and characteristics still remain to be determined and which could potentially have applications for space propulsion. However, more realistic theoretical models must first be developed to explain their existence and properties before applications of interest to NASA can be assessed and developed. 1. Introduction This report describes the analysis by MSE Technology Applications, Inc. (MSE) of the Electron Spiral Toroid (EST) concept being developed by Electron Power Systems Inc. (EPS). This analysis was conducted for the National Aeronautics and Space Administration's Langley Research Center (NASA-LaRC). The company received a Phase I award from the NASA Institute for Advanced Concepts (NIAC) – grant number 07600-013. The information regarding the EST concept is somewhat sketchy, since there are no peer-reviewed publications. Our first analysis of the concept was completed in November 1999, and was based on the limited literature available at the time; primarily a theoretical description of the concept by C. Chen [1], the NIAC Phase I report [2], as well as an EPS document describing other aspects of the concept [3]. After the release of an earlier version of this report and a discussion with EPS investigators [4], further information was made available [5,6] and subsequently reviewed. Finally, a meeting took place with EPS and the Massachusetts Institute of Technology (MIT) [7] during which the latest, nonpublished information [8,9] was made available. Note also that references [3,5,8] are different versions of a similar document; the revisions were made following the results of the present analysis. In the original "published" documents [1-8], it is claimed that a "stable" plasma, capable of storing vast amounts of energy, can be created without the need for external confinement (i.e., "free" ESTs). There is no exact definition of "stable", but indications from the available literature [2,3] suggest lifetimes of the order of years. Since plasmas in laboratories are notoriously short-lived entities, this claim is quite spectacular. Other claims are similar in scope. For example, the EST specific energies could be of the order of 6×10^16 J/kg. By comparison, combustion of 1 kg of hydrogen with oxygen would generate 1.2×10^8 J, which is equivalent to the liberation of approximately 1.25 eV/atom. To reach the claimed level of specific energy, each atom would have to be able to store 650 MeV of energy (approximately 60% of the rest-mass of the proton itself)! To date, only antimatter is known to have this level of energy density. The stored energy would primarily be in the form of a confined magnetic field, of the order of 16,000 Tesla. This would lead to an internal pressure of 1 billion atmospheres, yet no external confinement method is mentioned. The plasma in the EST is basically contained within a toroidal shell, with the electrons at high velocity in the poloidal direction (i.e., in orbit around the centerline of the torus). The electron motion generates a magnetic field along the toroidal direction, which forms the greater circle of radius R_T. A schematic of the concept is shown in Figure 1 below (taken from [2]). 2. Fundamental Dynamics The plasma is assumed to be strongly coupled. The analysis of plasma dynamics in [1] is based only on the cold-fluid model, which is certainly valid for strongly coupled plasmas. It is sufficient to say that thermal effects are assumed to be nonexistent or negligible, and therefore, they are not considered in [1] or in the present analysis. The toroid of inner radius r_b and outer radius R_T, shown in Figure 1, can be approximated by an infinitely long cylinder. The examination of the stability properties of the toroid can then be reduced to a two-dimensional problem. As described in [1], the plasma is considered to be within a toroidal shell, between the boundary radius r_b and an inner boundary r_1. The plasma is therefore contained in a cylindrical shell. This configuration is identical to the one described in [1]. Consider also the transformation from an orthogonal coordinate system (x̂, ŷ, ẑ) into a cylindrical coordinate system (r̂, φ̂, ẑ), as shown in Figure 2. The associated transformation matrix R_φ describes a rotation by an angle φ, such that: (u_x \ u_y) = R_φ (u_r \ u_φ) = (cos φ -sin φ \ sin φ cos φ) (u_r \ u_φ) (1) (u_r \ u_φ) = R_φ^-1 (u_x \ u_y) = (cos φ sin φ \ -sin φ cos φ) (u_x \ u_y) (2) and (∂_x \ ∂_y) = R_φ (∂_r \ r^-1 ∂_φ) (3) The equation of motion for a cold, incompressible plasma fluid is: ∂u_α/∂t + (u_α · ∇) u_α = (Z_α e_α / m_α) (E + u_α × B) (4) where α = e,i is the index for the plasma component (electrons and ions). The dynamical Equation (4) can then be expressed in the cylindrical coordinate system, using the fact that the magnetic field has a component in the ẑ direction only: ∂_t u_r + u_r ∂_r u_r - u_φ^2/r = (Z_α e / m_α) (E_r + u_φ B_z) (5-a) ∂_t u_φ + u_r ∂_r u_φ + (u_r u_φ)/r = (Z_α e / m_α) (E_φ - u_r B_z) (5-b) Since one is interested in steady equilibrium conditions, the time-derivatives and the radial velocity are assumed to be identically zero. The equilibrium configuration being symmetric, we also have E_φ = 0. The only velocity is in the φ̂ direction, the only electric field is in the r̂ direction only, and the magnetic field is in the ẑ direction. Therefore, one can drop the spatial index for these quantities. Assuming a single species of ions of mass m_i, we then have: u_e^2 / r = - (e / m_e) (E + u_e B) (6-a) u_i^2 / r = (Z_i e / m_i) (E + u_i B) (6-b) The electric field is given by Poisson's equation, i.e.: (1/r) ∂_r (rE) = (e / ε_0) (Z_i n_i(r) - n_e(r)) (7) At this stage, it is useful to introduce density scales n̄_e, n̄_i and bring all the spatial dependence into normalized functions f_e(r), f_i(r), such that: n_e(r) = n̄_e f_e(r); Z_i n_i(r) = n̄_i f_i(r) and Δf(r) = f_i(r) - f_e(r) (8) A spatial scale is also introduced as the minor radius of the toroid, r_b, and a normalized radial variable defined as: ρ = r / r_b; 0 ≤ ρ ≤ 1 (9) Introducing also the plasma frequencies ω_pe, ω_pi: ω_pe^2 = (e^2 n̄_e) / (m_e ε_0); ω_pi^2 = (Z_i e^2 n̄_i) / (m_i ε_0) (9) Poisson's equation becomes: (eE / m) (ρ) = (ω_pe^2 r_b^2 / r) [∫_0^ρ dρ' ρ' Δf(ρ')] = (ω_pe^2 r_b^2 / r) Φ(ρ) (10) The solutions of the equations of motion then become: u_e(ρ) = (r/2) [ω_ce ± √(ω_ce^2 + 4 ω_pe^2 Φ(ρ) / ρ^2)] (11-a) u_i(ρ) = (r/2) [-ω_ci ± √(ω_ci^2 - 4 ω_pi^2 Φ(ρ) / ρ^2)] (11-b) where the definitions of the cyclotron frequencies have been used: ω_ce = eB / m_e; ω_ci = δ ω_ce with δ = Z_i m_e / m_i (12) Finally, the magnetic field is given by Ampere's law: ∂_r B = -e μ_0 (n̄_i f_i u_i - n̄_e f_e u_e) (13) Assuming that the plasma is nearly neutral, one can set n̄_i = n̄_e, with any space-charge effects included in the distribution functions f_i, f_e. In that case, the evolution of the magnetic field becomes: ∂_r ω_ce = - (ω_pe^2 / c^2) (f_i u_i - f_e u_e) (14) 3. The EST Configuration According to ref. [1], the EST is characterized by an electron density function of the form: f_e(ρ) = { r_b/r if r_1 ≤ r ≤ r_b; 0 otherwise } (15) The ions form a background density with the same spatial dependence as the electrons, albeit with a slight relative excess f̂, such that: f_i(ρ) = f̂ f_e(ρ) (16) In that case, Φ(ρ) = ∫_(r_1/r_b)^ρ dρ' ρ' Δf(ρ') = (r_1 / r_b) (f̂ - 1) (ρ - r_1/r_b) (17) and Φ(ρ) / ρ^2 = (f̂ - 1) (r_1/r) (1 - r_1/r) (18) Although there is no other explicit information regarding the ions in the EST model, it is assumed that they provide a fixed background since the ion equation of motion is not being considered in [1]. It should also be pointed out that there is a somewhat confusing statement in [2], where the parameters of a large-scale EST are listed (page 11 of ref. [2]). Although the total charge is 186 coulombs, the system is called "charge-neutral". Even though the relative deviations from neutrality would appear small, the densities considered in these intense EST configurations lead to a large amount of electrostatic energy. In fact, it is precisely this electrostatic charge that is responsible for containment of the plasma and storage of the intense (16,000 Tesla!) magnetic field. At sufficiently large distances from the EST, the electric field given by the EST can be approximated by the zeroth-order term in the multipolar expansion: E ≈ Q / (4 π ε_0 R^2) (19) which (for the 186 Coulombs quoted in [2]) gives a field of E ≈ 1.7×10^12 V/m at 1 m distance. It is not known how the developers of the EST intended to prevent electrical discharges from spontaneously occurring between the EST and its surroundings, given this level of field intensity. Nevertheless, the theoretical analysis of the EST concept, as described in [1], can be continued. It is useful to introduce further normalization parameters, such that: v_e = u_e / (ω_pe r_1); v_i = u_i / (ω_pe r_1) (20-a) and Ω̂_ce = ω_ce / ω_pe; Ω̂_ci = ω_ci / ω_pe (20-b) Instead of normalizing the distance to the boundary of the toroid (Equation (9)), one can scale the distance with respect to the inner radius of the electron shell, as in [1]: ρ = r/r_1. In that case, the electron velocity is given by: v_e = (ρ/2) [Ω̂_ce ± √(Ω̂_ce^2 + 4 (f̂ - 1) (1/ρ) (1 - 1/ρ))] (21) Introducing the coupling parameter: α = (ω_pe^2 r_1^2) / c^2 (22) and since the ions are fixed, the equation for the magnetic field can simply be written as: ∂Ω̂_ce / ∂ρ = α (v_e / ρ) (23) and therefore: ∂Ω̂_ce / ∂ρ = (α/2) [Ω̂_ce ± √(Ω̂_ce^2 + 4 (f̂ - 1) (1/ρ) (1 - 1/ρ))] (24) Equations (21) and (24) describe the evolution of the system and are completely identical to Equations (23) and (24) of ref. [1]. Table 1: List of cases studied by Chen in [1]. Case # | α | f̂-1 | r_2/r_1 | r_1 (m) | R_T (m) 1 | 1.6 | 2×10^-2 | 1.01 | 4.95×10^-4 | 2.5×10^-3 2 | 10^3 | 1×10^-4 | 1.01 | 1.00×10^-2 | 0.10 3 | 2×10^4 | 4×10^-5 | 1.05 | 1.50×10^-2 | 0.15 4 | 4×10^6 | 5×10^-7 | 1.05 | 1.50×10^-2 | 0.15 Table 2: Comparison of our numerical results with those of Chen in [1]. Case | U_e(r_2) (m/s) [Chen] | U_e(r_2) (m/s) [current] | B_θ(r_1) (T) [Chen] | B_θ(r_1) (T) [current] | N_e [Chen] | N_e [current] 1 | 5.37×10^6 | 5.39×10^6 | 6.60×10^-4 | 6.64×10^-4 | 2.24×10^10 | 4.50×10^10 2 | 9.49×10^6 | 9.48×10^6 | 1.49×10^-2 | 1.48×10^-2 | 5.61×10^14 | 1.11×10^15 3 | 6.00×10^7 | 5.99×10^7 | 0.69 | 0.70 | 1.68×10^17 | 1.67×10^17 4 | 9.51×10^7 | 9.48×10^7 | 21.2 | 15.58 | 3.36×10^19 | 3.34×10^19 4. Stability Problems Both the dynamical equations and the numerical solutions of ref. [1] have been recovered, which would seem to bring some validity to the EST concept. However, it is crucial to examine the dynamical behavior of the complete system of equations including the ions! A key assumption barely mentioned in [1] is that the ions form a fixed background. However, since the magnetic field vanishes at the boundary of the toroid, there is no confining force being applied to the ion fluid near the surface. Since the toroid is also positively charged (the electrostatic force provides the confining force for the electrons), there is a strong repulsion pushing the ions outward. Therefore, there is no mechanism for keeping the ions inside the toroid. They would very rapidly "evaporate", thereby leaving the toroid absolutely charge-neutral. This process would also eliminate the confining force for the electrons, and the whole toroid would then rapidly expand, unable to contain the magnetic pressure. To look at the ion dynamics, consider Equations (5-a,b). For no initial azimuthal (i.e., poloidal) velocity (u_iφ = 0), and since E_r > 0 (f̂ > 1 for electron confinement), Equation (5-a) clearly yields ∂_t u_r > 0, and the ion gas is rapidly expanding. The fixed ion background assumption is therefore completely invalid for ion-motion time scales. One could then argue that a stable solution could still be achieved, but with the ions in motion. It is clear that as ions gain a radial velocity, the Lorentz force will also act to provide them with an azimuthal velocity (see Equation (5-b)). In that case, one must examine the stable solution of the ion fluid with an azimuthal velocity. The ion solution has already been described in Equation (11). Using the same normalization (20-a,b), one obtains (for the same density distribution): v_i = (ρ/2) [-Ω̂_ci ± √(Ω̂_ci^2 - 4 (f̂ - 1) (1/ρ) (1 - 1/ρ))] (28) Using (12), this can also be written as: v_i = δ (ρ/2) [-Ω̂_ce ± √(Ω̂_ce^2 - (4/δ) (f̂ - 1) (1/ρ) (1 - 1/ρ))] (29) A stable solution is possible if the discriminant remains positive, i.e., if: Δ_i = Ω̂_ce^2 - Ψ^2 ≥ 0 (30) with Ψ^2 = (4/δ) (f̂ - 1) (r_1/r) (1 - r_1/r) (31) Obviously, since the field vanishes at r = r_b2, Ω̂_ce = 0 and the condition cannot be satisfied. In fact, there will be a region of finite extent near the outer boundary, where this condition cannot be satisfied. The size of this region depends on the parameters α and f̂ - 1. Figures 9 and 10 show plots of both Ω̂_ce^2 and Ψ^2 for Cases #3 and #4 of Table 1. The allowed region where a physical solution can be found for the ions is determined by the distance between the origin (r = r_1) and the point at which the two curves cross each other. For Case #3 (Figure 9), it appears that most of the plasma in the shell would be unstable to ion "evaporation". For Case #4, this region is much smaller. One could argue that for the right choice of parameters, the unstable region would be reduced to a "skin". However, this does not solve the problem since the ions would always be emitted from the surface of the EST. As the relative charge ratio f̂ drops, the electrostatic confining force would also drop, and the torus would rapidly expand under the pressure of its own magnetic field. As the EST surface increases during expansion, so would the rate of ion loss. As pointed out by Chen [4], the discussion of ion stability can be avoided altogether by invoking the Virial theorem ([10], pp. 72-74), which states that a plasma cannot be self-confined. However, we believe that the examination of the dynamical equations elucidates the origins of the self-confinement problem better than maybe simply quoting a theorem. 5. The EPS Theoretical Model Before discussing further the implications of the cold-fluid model, it is worth investigating another theoretical model of the EST proposed by EPS, as described in [5,8]. This is an attempt at constructing a "discrete" model using a summation over a finite number of particles. The ions and electrons reside in separate shells (the ions form the inner shell), composed of a large number of loops of radius r_0, and a large number of particles along each loop. The spacing between electrons on a loop is d_e, and therefore, the number of electrons in a loop is: N_(e(loop)) = 2 π r_0 / d_e (35) The number of loops in the toroid is approximately (R_T >> r_0): N_(loop) = 2 π R_T / (k_0 d_e) (36) where k_0 d_e is the spacing between loops, with k_0 ≈ 1. The total number of electrons is then: N_e = N_(e(loop)) N_(loop) = (4 π^2 r_0 R_T) / (k_0 d_e^2) (37) Note that the EST surface area is also given by: Area = 4 π^2 r_0 R_T (38) The EPS investigators first compute the force acting on an electron in a single loop: F_e = (e^2 / (4 π ε_0)) 2 ∑_(n=1)^(N_(e(loop))/2) sin(n δθ / 2) / d_n^2 (39) Using small angle approximation, EPS writes: F_e ≈ (e^2 / (4 π ε_0 r_0 d_e)) [1 + 1/2 + 1/3 + 1/4 + ...] (40) Strictly speaking, this is a diverging series. EPS arbitrarily estimates the summation to be ≈ 5. However, this expression is wrong because it neglects neighboring loops and the logarithmic divergence. The proper way to evaluate these forces in the same limit of large N_e is to integrate Poisson's equation, giving: E = e / (ε_0 k_0 d_e^2) and F_e = e^2 / (ε_0 k_0 d_e^2) (49) The magnetic force on each electron is: F_M = (μ_0 e^2 v^2) / (k_0 d_e^2) = (e^2 / (ε_0 k_0 d_e^2)) (v^2 / c^2) (52) Analysis of the ion shell shows that centrifugal and magnetic forces are of the order of v_i v_e / c^2 and are far too weak to balance electrostatic repulsion, yielding no stable physical solution for the ion shell. Evaluating the required confinement pressure P_conf to balance the ion repulsion: P_conf ≈ f̂ P_mag (511 / E_e[keV]) (65) Unless electrons are ultrarelativistic, the required mechanical confinement pressure must be several times larger than the internal magnetic field pressure, making energy storage in near-vacuum or with weak vessels completely impractical. 6. Scaling Properties Approximate scaling relationships obtained from the numerical solutions: E_(e,max) ≈ 2.56×10^5 (r_b2/r_1 - 1) (α / 10^11) ((f̂ - 1) / 10^-8) keV (68) B_max ≈ 1.09×10^5 ln(r_b2/r_1) [(α / 10^11) ((f̂ - 1) / 10^-8)]^(1/2) Tesla (69) The condition for strong coupling: Γ = (1 / kT) (e^2 / (4 π ε_0 R)) > 170, with R^-1 = [(4/3) π n_p]^(1/3) (70) This implies T ≈ 2 K, presenting an extraordinary engineering challenge for beam injection or arc discharge formation. 7. Energy Storage and Lifetime Table 3: EST parameters listed in [2]. Parameter | Value Diameter, major, r_T | 0.63 m Diameter, minor, r_0 | 0.21 m Electron energy | 10 keV Total Mass | 1.86×10^-6 kg Magnetic Field | 16,000 Tesla Energy Loss, Radiation | 1.16 J/sec Energy Loss, Collisions | 8.9×10^-10 J/sec Total Energy | 1.9×10^12 J Table 4: Typical structural parameters satisfying energetic values in Table 3. r_2/r_1 | α | f̂-1 1.01 | 5.57×10^15 | 7.0×10^-16 1.05 | 1.16×10^15 | 6.7×10^-16 Inconsistencies: 1. The mass corresponds to n_e ≈ 1.7×10^23 m^-3 and B_eq ≈ 132 T, severely conflicting with the claimed 16,000 T. 2. To achieve 16,000 T, α must be ~10^15, requiring electron densities n_e > 6×10^29 m^-3 (higher than solid copper). 3. Collisional energy loss rate from Coulomb collisions: dE_e/dt ≈ 10^-12 J/s ≈ 7000 keV/s, giving a total loss rate Ė_EST^col ≥ 10^9 J/s (18 orders of magnitude larger than claimed 8.9×10^-10 J/s). Electron lifetime against collisions is ~1.4 ms, not years. 4. Cyclotron radiation loss rate: Claimed is 1.16 J/s; actual numerical integration gives ~4×10^7 J/s. 5. Gas kinetic confinement requirements: To contain ions at the boundary, a neutral gas pressure of ~9×10^13 Pa (~900 million atmospheres) is required. 6. Virial theorem: Plasmas cannot self-confine without massive external pressure or negative energy terms (e.g. gravity). 8. Experimental Observations In DSWA report [6], EPS described generating ESTs via a 400 A carbon arc discharge in low-pressure (0.0011 atm) Nitrogen. Luminous ring-like objects were photographed. Discrepancies and Issues in Experimental Claims: - Claimed energy loss rate of 1.89×10^-7 J/m^2 (meaning W/m^2) was calculated by multiplying power by surface area instead of dividing, underestimating emitted power density by 8 orders of magnitude (true value is ~19 W/m^2). - Observed objects were claimed to be unaffected by electric fields (charge neutral) and followed parabolic trajectories under gravity (a_buoy ≤ 0.5 m/s^2). However, the theoretical charge excess (f̂-1 = 7×10^-5) in an applied field of 200 V over 10 cm would produce an electric acceleration of a_elec ≈ 5×10^5 m/s^2 (6 orders of magnitude larger than gravity). Thus, observed neutral objects cannot possess the charge or trapped magnetic fields of the theoretical EST. - Observed luminous toroidal structures are likely benign fluid vortices ("smoke rings") or standard plasmoids rather than high-energy self-confined ESTs. 9. Conclusions MSE's conclusions regarding the analytical and experimental data published by EPS and MIT regarding the EST concept are as follows: (1) The cold-fluid equations for the electron gas and their numerical solutions (described in [1]) have been verified. MSE's numerical solutions agree with Chen's on this point. (2) However, the model in [1] does not describe the complete dynamics of the system. Within the context of that model, the ionic component is unstable in the presence of the required electrostatic field. Confining both electrons and ions requires an external confining field of the same order as the internal stored field. (3) The discrete model proposed by EPS contains fundamental errors. In the proper large-N limit, the ions cannot be naturally confined. (4) An external mechanical pressure of the same order of magnitude as the stored energy density is required to confine the ions, eliminating the possibility of confinement in a vacuum or partial vacuum. (5) Radiative emission or boundary fluctuations cannot provide confinement under the Virial theorem without causing rapid collapse via radiative losses. (6) The requirement for an external pressure of the same order as the contained energy density negates any practical energy storage applications. (7) Excessive energy losses through Coulomb collisions (electron lifetime ~1 ms) and cyclotron radiation prevent long-term stability. (8) Claims of suppression of electron-ion collisions due to strong coupling are invalid due to the large relative velocity between electrons and ions. (9) Continuous ionization models to maintain a fixed ion background lead to staggering particle/energy loss rates (10^32 particles/s, ~2.3×10^14 J/s) and sub-microsecond lifetimes. (10) Published numbers are inconsistent and unphysical. The experimental evidence does not support the existence of high-energy ESTs, though observed metastable plasmoids/vortices warrant cautious, peer-reviewed scientific study. 10. References [1] C. Chen, "Equilibrium and Stability Properties of Cold-Fluid Electron Spiral Toroids", Electron Power Systems, Inc., 1999. [2] C. Seward, "Low Cost Transportation using a Stable Plasma for Energy Storage", NASA report, NIAC-CP-98-01, May 1999. [3] D. C. Seward, "Energy Storage Using the Electron Spiral Toroid", EPS Inc. pub., Sept 1999. [4] C. Chen and C. Seward, private communication. [5] D. C. Seward, "Energy Storage using the Electron Spiral Toroid", EPS Inc. pub., Jan. 2000. [6] C. Seward, "The Electron Spiral Toroid (EST) for Energy Storage", Final Report to DSWA, October 1998. Contract # DSWA01-97-M-0537. [7] C. Chen, C. Seward, D. C. Seward and W. J. Guss, private communications, MSE/EPS/MIT Meeting, MIT, May 25, 2000. [8] D. C. Seward, "Energy Storage using the Electron Spiral Toroid", EPS Inc. pub., May 2000. [9] C. Chen, "Equilibrium and Stability Analysis of Intense Electron Spiral Toroids", presented at the MSE/EPS/MIT meeting [7]. [10] G. Schmidt, Physics of High-Temperature Plasmas, Academic Press, NY, 1966. [11] T. J. Dolan, Fusion Research, Volume 1 - Principles, Pergamon Press. [12] N. Krall & A. Trivelpiece, Principles of Plasma Physics, San Francisco Press, CA, 1986. [13] J. D. Jackson, Classical Electrodynamics, J. Wiley, New York (1975). [14] S. Gilbert, J. Bollinger and D. Wineland, "Shell-Structure Phase of Magnetically Confined Strongly Coupled Plasmas", Phys. Rev. Letters, vol. 60, 2022 (1988). [15] See for example: S. Ichimaru, Rev. Mod. Phys., vol. 54, 1017 (1982). [16] M. Berger and S. Seltzer, "Tables of Energy Losses and Ranges of Electrons and Positrons", NASA SP-3012 (1964). [17] See for example: W. Bostick, "Plasmoids", Sci. American, vol. 197 (Oct. 1957). [18] See for example: P. A. Silberg, J. Appl. Phys., vol. 49 (1978), 1110. [19] See for example: "Science of Ball Lightning", ed. Y.H. Ohtsuki, World Scientific pub., Singapore, 1989. [20] V. D. Shafranov, Sov. Physics JETP, vol. 6 (1958), 545. REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 1. AGENCY USE ONLY: Blank 2. REPORT DATE: December 2000 3. REPORT TYPE AND DATES COVERED: Contractor Report 4. TITLE AND SUBTITLE: Theoretical Analysis of the Electron Spiral Toroid Concept 5. FUNDING NUMBERS: PO L-8871, WU 522-17-41-20 6. AUTHOR(S): Jean-Luc Cambier and David A. Micheletti 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES): MSE Technology Applications, Inc., 200 Technology Way, P.O. Box 4078, Butte, MT 59702 8. PERFORMING ORGANIZATION REPORT NUMBER: NASA-32 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES): National Aeronautics and Space Administration, Langley Research Center, Hampton, VA 23681-2199 10. SPONSORING/MONITORING AGENCY REPORT NUMBER: NASA/CR-2000-210654 11. SUPPLEMENTARY NOTES: Langley Technical Monitor: Dennis M. Bushnell 12a. DISTRIBUTION/AVAILABILITY STATEMENT: Unclassified-Unlimited, Subject Category 75, Distribution: Standard. Availability: NASA CASI (301) 621-0390 13. ABSTRACT: This report describes the analysis of the Electron Spiral Toroid (EST) concept being promoted by Electron Power Systems Inc. (EPS). The EST is described as a toroidal plasma structure composed of ion and electron shells. It is claimed that the EST requires little or no external confinement, despite the extraordinarily large energy densities resulting from the self-generating magnetic fields. The present analysis is based upon documentation made available by EPS, a previous description of the model by the Massachusetts Institute of Technology (MIT), and direct discussions with EPS and MIT. It is found that claims of absolute stability and large energy storage capacities of the EST concept have not been substantiated. Notably, it can be demonstrated that the ion fluid is fundamentally unstable. Although various scenarios for ion confinement were subsequently suggested by EPS and MIT, none were found to be plausible. Although the experimental data does not prove the existence of EST configurations, there is undeniable experimental evidence that some type of plasma structures whose characteristics remain to be determined are observed. However, more realistic theoretical models must first be developed to explain their existence and properties before applications of interest to NASA can be assessed and developed. 14. SUBJECT TERMS: Physics, Plasma Physics, Plasma Applications, Energy Storage, Propulsion 15. NUMBER OF PAGES: 42 16. PRICE CODE: A03 17. SECURITY CLASSIFICATION OF REPORT: Unclassified 18. SECURITY CLASSIFICATION OF THIS PAGE: Unclassified 19. SECURITY CLASSIFICATION OF ABSTRACT: Unclassified 20. LIMITATION OF ABSTRACT: UL