Electrostatic plasma confinement

The question of the priority of the application of inertial-electrostatic systems for the implementation of nuclear reactions and the direct conversion of the energy of these nuclear reactions into electrical energy has not yet been resolved.

In the USSR, these proposals were first formulated by O. A. Lavrentiev , in his note sent to the Central Committee of the CPSU (B.) On July 29, 1950 ^[2] . In his note, O.A. Lavrentyev proposed lithium-hydrogen reactions as promising from the point of view of nuclear fusion for the fusion bomb: p + 7Li = 24He + 17.2 MeV and D + 6Li = 24He + 22.4 MeV on the basis of, so called, the method of "free collision of nuclei". It was this proposal that aroused the political leadership of the project (who had similar intelligence information on the American nuclear project) interest in the novice scientist, which allowed O.A. Lavrentyev to enter Moscow State University and start a scientific career.

According to A. D. Sakharov, who gave his feedback on the proposals, the scientific content of this note by O. A. Lavrentiev was trivial. It really contained only one original proposal of “electrostatic absorption of energy of fast particles in a slowing electric field” for selecting the electrical power of nuclear reactions carried out in a “gas” (plasma) volume held by an electrostatic field.

In his note, O. A. Lavrentyev proposed that the volume in which nuclear processes take place was surrounded by two conducting shells (the inner shell — the grid cathode) to which a potential difference of 0.5–1 MV is applied. According to O. A. Lavrentyev, positively charged nuclei accelerated during nuclear reactions, flying through the grid, must fall into a slowing electric field and, either without energy loss, be thrown back into the volume in which nuclear processes take place, or reach the outer shell, creating in the EMF circuit.

In the absence of other losses, the condition for maintaining the reaction is the excess of the energy released during nuclear reactions, over the energy selected by the system of two shells.

According to O. A. Lavrentyev, since in this situation the energy loss is proportional to the shell area (direct hits of the products of nuclear reactions), and the energy released during nuclear reactions is proportional to the volume, it is always possible to choose such installation dimensions that with constant external power consumption the condition of maintaining the reaction will be fulfilled.

The proposal made by OA Lavrentiev, however, did not take into account the loss of energy due to radiation, as well as the emission of neutral particles that carry away a significant portion of the energy. It was also problematic at that time, and even now the technical possibility of a structural solution that provides thermal stability for the internal grid remains.

For historical reasons, the proposed methods of electrostatic confinement of products of nuclear reactions to produce electrical energy have not received priority development in Soviet science.

At the time of the formulation of these abstract sentences, O. A. Lavrentyev did not have a higher education and did not possess the necessary theoretical, and even more practical, knowledge base.

After the death of I. V. Stalin and the execution of L. P. Beria, having lost political patronage, he failed to develop his own ideas into a large-scale state significance, and A. D. Sakharov and I. E. Tamm were interested in developing their own ideas purely magnetic confinement of thermonuclear plasma, where technical and physical problems, as it turned out, was objectively not less.

Having obtained the distribution after graduating from the Moscow State University to the Kharkov Physical-Technical Institute of the Academy of Sciences of the Ukrainian SSR, O.A. Lavrentiev continued in the period 1953-1960, mainly experimental studies of electrostatic and also magneto-electrostatic confinement of thermonuclear plasma ^[3] .

The scheme of electrostatic traps of high-temperature plasma for the purposes of industrial fusion was proposed by O. A. Lavrentyev on June 22, 1950, and the electromagnetic trap of high-temperature plasma in the form of an open magnetic trap with electrostatic locking of magnetic slots - in March 1951.

Publications on these issues in Ukrainian were published in the Ukrainian Physical Journal in 1963 ^[4] .

In a simple electrostatic trap, plasma ions are held by an external electric field applied between an internal spherical cathode grid and an external spherical electrode, on the surface of which additional sources of ions are placed ^[5] .

In order to increase the number of ions retained in an electrostatic trap, O. A. Lavrentyev proposed a modification of an electrostatic trap with reversed polarity, for which he considered it necessary to ensure fundamentally strict sphericity of the ion-optical system and strict spherical focusing of ionic and electronic streams injected into the system.

A diagram of a simple electrostatic trap with reversed polarity, proposed by O. A. Lavrentiev, is shown in fig. 1. In this device, a high positive potential of 20-100 keV is applied to the inner electrode - 2, which is a double half ring. The chamber is pumped out to a high vacuum, and then filled with working gas. As a result of focusing the flow of charged particles, a dense high-temperature plasma is formed in the center, far from the surface of the electrodes. Intensive thermonuclear reactions are carried out in the center, and near the electrodes the plasma density is many orders of magnitude lower and should not exceed the limit value determined from the condition of a moderate thermal load on the electrodes. The outer electrode - 1 is made in the form of two hemispheres with water cooling. Data on the operating parameters of the installation in [5] are not given.

OA Lavrentiev put forward the following theoretical assumptions about possible physical processes in simple electrostatic traps with reversed polarity.

Thermonuclear plasma is formed in the center of the system as a result of focusing the flow of charged particles. In such a plasma, subject to strict radial focusing and spherical symmetry of the system, virtual electrodes — cathodes and anodes can occur. They possess the properties of real electrodes, but practically do not introduce losses into the streams of charged particles circulating through them.

Virtual electrodes must be formed in the drift space if the density of the flux of charged particles injected into the plasma is sufficiently large. The first virtual electrode (anode) is formed in the specified system by the positive column of the plasma glow gas discharge arising between the internal anode and the external cathode. The electrons emitted inward from the surface of the sphere, passing through it, must form a second virtual electrode (cathode). Part of the ions of the virtual anode, accelerated by the electric field between the virtual anode and the virtual cathode should form the third virtual electrode (anode).

Fig.1 Simple electrostatic trap. 1 - cooled cathode, 2 - anode.

Between virtual electrodes as well as between real ones, charged particles can accumulate, increasing the initial flow many times.

In the simple electrostatic trap with reversed polarity shown in Fig. 1, the virtual electrodes are not distorted by the grid structure, therefore the number of virtual electrodes should increase both with increasing device dimensions and increasing flux of injected ions, but with each new electrode the plasma density increases and, therefore , neutron source output.

Indeed, the solution of the Poisson equation gives an oscillating curve for the potential. This is evident from the following considerations. For a two-stream plasma system in spherical geometry with a radial coordinate r, the Poisson equation for potential V is as follows (ρe and ρi are the charge densities of electrons and ions, respectively):

(1 / r2) (d / r [r2 (dV / dr)) = 4π (| ρe | -ρi), (1)

If we take for 0 the potential on the virtual anode, then from the energy conservation equation follows:

½Mvi2 = | eV (r) |, (2) ½mve2 = e (V-V0), (3)

where V0 is the potential at the cathode, M and m are the mass of ions and electrons, e is the electron charge. From the condition of charge conservation it follows (Ie, i is the electron and ion currents, ve, i are the velocities of the ions and electrons):

Ie, i = 4πr2ρe, ive, i, (4)

We will carry out the normalization of the radius and potential:

f (r) = V (r) / V0, (5)

R = r / r0, (6)

where r0 is the radius of the virtual anode, f (r0) = 0. Then the relation (1) can be rewritten in the form:

d2f / dR2 + (2 / R) (df / dR) = (K + / R2) (f-1/2-λ + (1-f) -1/2), (7)

K + = Ii / | V0 | 3/2 (M / 2e) 1/2 = 4πr2ρif1 / 2 / | V0 |, (8)

λ + = (Ie / Ii) (m / M) 1/2, (9)

Fig.2. The calculated graph of the normalized potential for K + = 0.7, λ + = λ + max and K + = 0.67, λ + = λ + max.

The parameters K + and λ + are not independent because of the need to satisfy the boundary conditions, and each K + corresponds to λ + max.

Fig.3. Graph of the localization of the parameters K + and λ +, determined by the boundary conditions.

The assumption of an increase in the density of the confined plasma with an increase in the number of virtual electrodes is illustrated in the graph of the normalized ion density ρi = ρi (4πrc2 / K + | V0 |), shown in Fig.5.

Fig. 5. Graph of normalized ion density ρi in a simple electrostatic trap.

It should be noted that these conclusions are valid for the situation when the motion of particles is strictly radial, and the system is spherically symmetric.

In a system with spherical focusing, due to the directional movement of particle fluxes to the center, their density increases as 1 / r2 up to a certain radius r0, which characterizes the accuracy of spherical focusing.

The power released in the reactions is proportional to the product of the plasma volume and the squared density and grows as 1 / r0 with improved focusing.

Taking into account the available empirical estimate in the range of energies that we are interested in, 0 <ε <150 kV, the dependence of the fusion reaction cross section with the participation of deuterons σf (ε), measured in barn, on the deuteron energy ε, measured in kV [6, Aleksandrovich E.-G. V., Sokovishin V. A., PTE, 1961, Vol.5, p. 7-25]: σf (ε) = 140 ∙ exp {-44.4 / ε1 / 2} / ε, it can be concluded that the nuclear reaction rate <σfv> in a certain energy interval weakly depends on r, then, starting from O. Lavrent'ev’s reasoning, who proposed to average out the power released in fusion synthesis over radius r, we obtain the following relation for this value: Pf = 4πR3Ef <σfv> ni2 (R / r0-1), where R is the radius of the outer sphere, ni - average density of ions, Ef - energy of a single act of nuclear reaction.

Reasoning that the degree of focusing of the ion flux depends on the quality of the electrode structure of the accelerating gap of the anode-cathode, as well as on the scattering of ions on top of each other, and the existing technological methods of forming ion fluxes with low divergence (multi-aperture ion sources) allow minimizing the influence of geometric parameters of structural elements to negligibly small, O. A. Lavrentiev came to the conclusion that the greatest contribution to the defocusing of an ion beam in an ideal electrostatic device would clearly be it Coulomb scattering of charged particles having the character of multiple interactions with deflection at small angles, that can be taken into consideration statistically. The path-averaged root-mean-square deviation of a particle from accurate radial motion is estimated as: <θ2> ~ (1 / E) 22πe4niLlnΛ, where lnΛ is the Coulomb logarithm, L is the mean free path of the ion before the collision with the grid, E is the average energy of the ion accelerated by the electrostatic field .

Hence, since it follows from the charge conservation law that nivi / n0maxv0 = ro2 / R2 ~ <θ2>, where vi and v0 are the thermal velocities of ions at the periphery and center of the device, n0max is the maximum achievable plasma density at the center of the electrostatic trap, and R >> r0, the value for n0max with spherical focusing of fluxes of charged particles limited by Coulomb scattering, is obtained as follows: n0max ~ (Ti / T0) 1 / 2E2 / 2πe4LlnΛ, where Ti is the plasma temperature in the positive column of the discharge, T0 is the plasma temperature inside focus areas.

It should be noted that, in his assessments, O. A. Lavrentiev did not very correctly assume that the temperatures inside the focusing region and in the plasma of the positive discharge column were equal in order of magnitude.

The estimate shows that in the ideal case, when the Coulomb scattering makes the largest contribution to the defocusing of the ion beam, the plasma density in the center will be many orders of magnitude greater than the plasma density at the periphery. However, with such densities, gas kinetic scattering will also become significant, which is also not taken into account in the above estimate.

The works [3 and 4] were translated into English and served as one of the motivations for R. L. Hersh in conducting the experiment, including the verification of theoretical positions expressed by O. A. Lavrentyev.

Returning to the priority dispute, it should be said that the American side claims [7, RL Hirsch, Inertial Electrostatic Confinement of Ionized Fusion, Journal of Applied Physics, V. 38, No. 11, p. 4522-4534, 1967] that for the first time the existence of a localized glow in the center of a spherically symmetric high-frequency electron-multiplying tube evacuated to high vacuum was observed by P.T. Farnsworth in 1934. A report on the observation of this effect was not published, on the observation of this effect P.T. Farnsworth in a private conversation told R. L. Hersh in 1964, associating this effect with the possibility of the formation of electron fluxes focused to the center of the cavity inside the hollow anode a potential well that retains and accumulates ions from the filling gas. P.T. Farnsworth allegedly suggested using this effect to hold and accumulate thermonuclear ions in a small volume in the mid-50s of the 20th century. The first theoretical publication, which studied the problems of spherically symmetric focusing of ion and electron fluxes in a system proposed in private communication by V.H. Wells in 1954 and independently, also in private communication, by P.T. Farsworth in 1956, published in the USA in 1959 [8, WCWatson, Jl Elmore, KMTuck, On the Inertial-Electrostatic Confinement of the Plasma, The Physics of Fluids, V.2, No. 3, p. 239-246, 1959]. The data on the experiment on spherically symmetric focusing of ion fluxes on an apparatus developed by R. L. Hersh [7] were published in 1967.

Open magnetic trap with electrostatic locking of magnetic slots

Open magnetic traps themselves have several advantages: high permissible ratio of plasma pressure to magnetic field pressure, plasma magnetohydrodynamic stability (in systems with the so-called "minimum B"), the ability to work in a stationary mode and relative constructive simplicity.

In the simplest version, an open magnetic trap is created by two identical coaxial coils connected in the same direction. In this case, the magnetic field between the coils is somewhat weaker than in the plane of the coils, so that the central part of the field is enclosed between two magnetic “traffic jams”, or “mirrors,” areas with a strong field. The ratio of the field in traffic jams W to the field in the central part of the B0 trap is usually called a cork or mirror ratio: α = Bm / B0.

In open magnetic traps, also called adiabatic, long-term retention of charged particles is based on the preservation of the transverse adiabatic invariant — the ratio of the particle transverse energy to the Larmor rotation frequency, or the physical parameter derived from this value — the magnetic moment of the Larmor circle. If there is no electric field, then when a charged particle moves in a magnetic field, its velocity ν remains constant (the Lorentz force, being perpendicular to ν, does not work). In addition, in a strong magnetic field, when the Larmor radius is ρ = v ﬩ / ωB (v ﬩ is the transverse velocity component with respect to B, ωB = eB / tc is the Larmor frequency, e is the charge of the particle, t is its mass, s is the speed of light is significantly less than the characteristic length of the change in the magnetic field, the value also remains: μ = t v2 ﬩ / 2 B.

This quantity, which also has the meaning of the magnetic moment of the Larmor circle, is an adiabatic invariant of quasiperiodic motion.

Since μ = const, as the charged particle approaches the plug, the transverse velocity component v ﬩ increases, and since ν = const, the longitudinal velocity component decreases and, for a sufficiently large α, it can vanish. In this case, the particle will be reflected from the magnetic tube.

Let us introduce into consideration the angle θ composed by the velocity vector with the direction of the magnetic field B. It is equal to (π / 2) - ψ, where ψ is the so-called stepping or pitch angle. It is easy to see that the magnetic tube reflects only those particles for which in the central part of the trap it is satisfied that: sin θ> α-1/2 = (B0 / Bm) 1/2.

All particles with angle θ less than θ0 = arcsin [(B0 / Bm) 1/2] fall into the "forbidden cone" of directions and fly out of the trap. Thus, the adiabatic trap holds not all particles, but only those that are inside the allowed cone of directions.

The particles held by the trap make relatively fast oscillations between the points of reflection and, at the same time, slowly transfer from one line of force to another, experiencing the so-called magnetic drift. The velocity of this drift is of the order of magnitude vm ~ vp / R, where ρ is the Larmor radius, R is the radius of curvature of the field line.

Thus, open magnetic traps have a major drawback: a short plasma lifetime due to its large losses along magnetic lines of force in the magnetic slots of the trap.

To reduce plasma losses through magnetic gaps, O. A. Lavrentiev proposed a method for electrostatic locking of magnetic gaps, which consists of the following.

In the region of the magnetic slit, the flow of charged particles is limited in the transverse direction by grounded electrodes, and behind the slit the flow is blocked by a negatively charged electrode (or a system of electrodes).

At a sufficiently high negative potential, electrons are reflected from this electrode (negative potential barrier) back into the trap, so that the only channel for the loss of electrons from the trap is their diffusion through a magnetic field.

As a result, the electron lifetime increases significantly, a negative space charge accumulates in the trap, and the plasma acquires a negative electrostatic potential.

Ions exit the trap through magnetic gaps (on negatively charged electrodes), but to even out the rate of loss of electrons and ions in the magnetic gaps, positive (ambipolar) potential barriers are automatically installed, reducing the loss of ions from the trap.

However, to establish such a pit-like distribution of the electrostatic potential, it is necessary that the transverse size of the particle flux in the gap should not be much larger than the Debye screening radius.

Otherwise, with a larger flow width, the barrier does not arise due to the large potential sagging in the gap, and the ions leave the trap without slowing down.

The necessary condition for the smallness of the transverse size of the magnetic slits can most easily be fulfilled for various acute-angled magnetic-pallet geometries created by a system of conductors with opposite current directions in adjacent conductors (in anti-microbotrons or multi-fields).

Such a combination of an acute-angled magnetic field with electrostatic locking of magnetic slots is called the “electromagnetic trap”.

Thus, in the electromagnetic trap, the electron component of the plasma is held by external magnetic and electrostatic fields, and the ion component is held by the electrostatic field of the space charge of uncompensated electrons. In this case, the lifetime of the plasma in the trap is determined by the rate of electron diffusion through the magnetic field, and the rate of ion loss adjusts to the rate of electron loss by controlling the values ​​of potential barriers in the magnetic gaps.

Along with the above-mentioned advantages inherent in the entire class of open traps, a specific feature of electromagnetic traps is the possibility of creating and heating a plasma by a simple method of injecting high-energy electrons (and under certain conditions and ions) through magnetic gaps. In this case, an acute angular magnetic field with its central region of non-adiabatic particle motion ensures the effective capture of injected flows. The captured electrons produce ionization of the working gas and give up some of their energy to the cold plasma. Such a "barrier" injection of electrons, produced from a negatively charged locking electrode-cathode, is the most energy-efficient compared to all other methods of creating and heating plasma in electromagnetic traps. This is due to the fact that electrons that go back to the locking electrode-cathode do not carry energy out of the trap (except for a small “above-barrier additive”), but give it to an electric field. Since simultaneously with the departure of electrons through the barrier, they are injected from the barrier, the electric field transfers the energy received from the outgoing electrons directly to the injected, returning it to the plasma without loss, that is, energy is recovered. The loss of energy by electrons is associated only with their diffusion through a magnetic field.

The logic of the development of scientific research led, finally, to O. A. Lavrent'eva to the idea of ​​multislit open magnetic traps of thermonuclear plasma with electrostatic locking of magnetic gaps [5, O Lavrentyev, V. A. Sidorkin, V. P. Goncharenko, Yu. S. Azovskiy, S. A. Vdovin, “Investigation of a multislit electromagnetic trap,” UFZh, 1974, v. 19, No. 8, p. 1277–1280].

The most well-known device using IEC is the Fuzor Farnsworth-Hirsch , described in 1967. ^[6] It consists of two concentric spiral electrically conductive grids in a vacuum chamber. A small amount of thermonuclear fuel is introduced into the chamber, which is ionized by the voltage between the grids. Positively charged ions are accelerated to the center of the chamber and a synthesis reaction may occur between them.

Fuzors are rather simple for making by amateurs or small laboratories. Fuzors are capable of producing thermonuclear reactions, but cannot produce any significant amount of energy. They are dangerous to handle, because use high voltage and can emit radiation (neutrons, gamma rays, x-rays). Fusors are used as commercial neutron sources, for example, under the brands FusionStar and NSD-Fusion.

There are several projects to solve the main problems inherent in the Fusors. In the original device, some ions collide with grids, heating them and contaminating the plasma with heavy ions. Polywell (Polywell) uses magnetic fields to create a virtual electrode. ^[7] In another project, the Penning Trap is used to capture electrons. ^[8] . The third project MARBLE ^[9] uses electrostatic optics to keep ions away from the grid conductors.

• University of Wisconsin-Madison IEC homepage
  • IEC Overview
• From Proceedings of the 1999 Fusion Summer Study (Snowmass, Colorado):
  • Summary of Physical Aspects of Emergency Concepts
• Inertial Electrostatic Confinement (IEC) of a Fusion Plasma with Grids
• Fusion from Television? (American Scientist Magazine, July-August 1999)
• Todd Rider's 1994 Masters Thesis
  • A General Critique of Inertial-Electrostatic Confinement Fusion Systems
• Latest Fusion developments (WB-7 - June 2008) based on the work of Dr. Robert Bussard