My Idea. How to Make TOKAMAK Viable Right Now

[Joseph Chikva]

The Method of Creation of Plasma and Ignition of Self-sustained Fusion Reaction in Toroidal Reactors

Abstract
[em]Unfortunately I can not upload the full text with drawings.[/em]

The proposing Method unlike to using now others comprises in usage for plasma creation and its further ignition the created in-situ halo-layer of high-energetic particles to the puffed gas.
For realization of Method the following procedures should be performed consistently and corresponding hardware should be included in toroidal fusion reactor:
In-situ creation of halo-layer:
• orthogonally to equatorial plane of toroidal vacuum chamber to create generally the time-dependent magnetic field (bending field) penetrating only its curvilinear segments,
• to apply axial (toroidal) magnetic field only in the regions located remotely from injection points,
• along the axis of toroidal vacuum chamber to inject 3 different kinds of pulse high current particle beams (two ions’ – reacting components and one – electron’s) with such a parity of particles’ kinetic energies allowing them the capability of moving in a given bending magnetic field on a common equilibrium orbit (gyro-radiuses (rg=p/qB) of all 3 spices are equal) in such a manner that faster ion beam passes through the moving at the same direction slower ion beam with sufficient for nuclear fusion collision energy and the relativistic electron beam moving oppositely to ions thus allowing to combined beam the self-focusing capability,
• to apply axial (toroidal) accelerating electric field compensating the occurring together with fusion two effects: tendency of alignment of velocities of reacting particles and also electrons’ energy losses via Bremsstrahlung.
G.I. Budker says that number density up to 10^24 m^-3 and even higher is achievable in combined beam and as result of fusion the high energetic fusion products are produced, from which neutrons escape reactor while charged particles form halo-layer.
For creation of plasma and its ignition at once after injection:
• from the walls with the help of corresponding valves to puff into the vacuum chamber the gas consisting the fuel components. And already being there halo-layer ionizes that gas and then generates the current similarly to that how current is driven by beam/beams of neutrals in modern TOKAMAKs.
• in regions being free from axial magnetic field to apply such a field at once after the end of injection.
The Method allows the reliable ignition of plasma in all kinds of toroidal fusion reactors.

[Joseph Chikva]

Background of the Invention

Fusion is the process by which two light nuclei combine to form a heavier one. The fusion process releases a tremendous amount of energy in the form of fast moving particles. Because atomic nuclei are positively charged – due to the protons contained therein – there is a repulsive electrostatic, or Coulomb, force between them. For two nuclei to fuse, this repulsive barrier must be overcome, which occurs when two nuclei are brought close enough together where the short-range nuclear forces become strong enough to overcome the Coulomb force and fuse the nuclei. The energy necessary for the nuclei to overcome the Coulomb barrier is provided by kinetic energies, which must be rather high.
For example, the fusion rate can be appreciable if the temperature is at least of the order of 104 eV—corresponding roughly to 100 million degrees Kelvin. The rate of a fusion reaction is a function of the temperature, and it is characterized by a quantity called reactivity. The reactivity of a D-T reaction, for example, has a broad peak between 30 keV and 100 keV.

Heating is needed during startup before alpha heating can take over.

And, so, we need to get the core of the plasma to 10keV i.e. around 100 million deg K, that for Plasma Volume 57.5-840 m3 (first number is of compact high field TOKAMAK IGNITOR, while the second is ITER’s – the largest TOKAMAK ever built) and 1020 m-3 Number Density corresponds to Plasma Stored Energy 11.9-520 MJ.

Existing (using) now plasma creation and heating methods
For TOKAMAKs and other fusion experiments using toroidal vacuum chambers (e.g. Large Helical Device – Stellarator)

Initial heating (Ohmic heating). Generated by induced electric field driving the toroidal current
When driving current using a toroidal electric field, current is initially driven at the surface (skin-effect) and then diffuses into the plasma.
Diffusion coefficient DJ = η/µ0 m2/s
Plasma resistivity (Spitzer) η=10-4Z lnΛT-3/2 Ωm and so:

DJ = ~103T-3/2 m2/s
During plasma startup some time is needed for diffusion from the edge to center. For a plasma on the scale of meters, at 10eV the timescale is 10ms and at 1keV it’s 10s of seconds [6]

Then resistive heating ηJ2 raises the temperature
But at the same time the resistivity of plasma decreases with temperature η 1/ T3/2
As the plasma heats up, the amount of energy which can be pumped into the plasma drops.

From the other side the energy losses increase by increasing the temperature – τE gets smaller.

Significant time is needed for Ohmic heating – big energy losses during that time mostly via Bremsstrahlung.

Neutral Beam Injection (NBI)
• Ions from the ion source accelerate by grids to high energy
• Then they pass through the neutraliser and become neutral high energy atoms
• The neutral beam penetrates the reactor magnetic fields. The penetration of the beam depends on the NBI energy, mass and on the plasma density
• Within plasma neutrals are ionized by collisions with thermal ions & electrons
• These fast ions are trapped by the reactor magnetic fields
Advantages
• Efficient heating of ions
• High power capability (40 MW on TFTR, 24 MW on JET, 70MW projected for DEMO)
• Drives plasma rotation (stabilizing lock modes)
• Fuelling
• Current drive
Disadvantages
• Heating not well localized
• Neutralizing cell is a gas filled chamber directly joining with vacuum vessel of reactor with long “atom conductor”. For preserving vacuum quality in a chamber vacuum absorbers on the walls of atom conductor are used which are needed desorbtion after each shot.

Ion Cyclotron Resonance Heating
Advantages
• Localised heating
• Hydrogen minority ICRH creates H minority with E> Ecrit – it heats electrons
• However, heating of IONS is also possible (e.g. 3He minority in DT plasma)
• Some current drive
Disadvantages
• Antenna inside the vessel
• Low power capability
• Plasma coupling may be a problem in, e.g. H-mode with ELMs
Concluding all three using now heating methods it can be said that all those need significant time for putting into the plasma the energy sufficient for ignition.
[em]So, today we already know how to confine plasma in toroidal reactors long enough time (3-5 sec has been really achieved) but we have not effective enough heating way: temperature limit of Ohmic heating goes not exceed 1 keV order, and RF heating and NBI have not enough power as even very powerful 70 MW NBI source will heat 840 m3 plasma in ITER with projected number density 2*1020 m-3 in 7.4 s even in 100% energy absorption case (100% is impossible by definition).

And it is proposed the conceptually new Method comprising in heating of plasma by creating in-situ in the reactor of high energetic halo-particles, with the help of which it is possible to input the required energy within only several milliseconds.[/em]

For providing of above mentioned the following procedures should be performed consistently (and corresponding hardware should be included in toroidal fusion reactor):

To create the bending magnetic field directed orthogonally to equatorial plane of toroidal vacuum chamber (vertically) penetrating only its curvilinear segments.
(As a rule the vacuum chamber of toroidal fusion reactors has a round central axis but generally round segments can alternate with the rectilinear – racetracks). And as the Method is proposing injection along the axis of high current beams, presence of racetracks would be preferable as they provide easier injection.
Such racetracks have been used in first Stellarators. Also they widely used in high energy particle accelerators for example racetrack FFAG betatron for Muon Fabric (Brookhaven National Laboratory) or Induction Synchrotron (All-ion Accelerator) developing now by KEK (High Energy Accelerator Research Organization)

[Joseph Chikva]

And it is proposed to create orthogonally to equatorial plane of vacuum chamber the bending magnetic field penetrating only its curvilinear segments. Such a field may be created by dipole magnets like to how similar purpose fields are created in synchrotrons or by betatron type magnet systems. The order of initial value of that field would be 0.1-0.4T. Then in the course of acceleration field’s induction should be increased correspondently to instant momentums of maintaining particles, thus keeping comparatively constant equilibrium radius.

To apply axial (toroidal) magnetic field only in the regions located remotely from injection points
Periodic axial magnetic field is needed for avoiding or slowing down of instabilities (e.g. two-stream instability)
As it is shown in number of papers [e.g. 9] that such a field dramatically expands stability area.
Beams injection points should be free from influence of that field but being injected particles should pass through that field in each turn.

To inject into the common axis (axis of vacuum chamber) 3 (three) pulse high current beams.
It is offered to inject two beams of particles of reacting components and to direct them along the same orbit and at the same direction but with different coherent motion velocities.
So, one faster ion beam should transit (pass) through another slower ion beam and their relative velocity should be sufficient for providing to reacting nuclei enough collision energy required for fusion (enough energy for Coulomb barrier overcoming).
For achievement of sufficient intensity of nuclear fusion the focusing of reacting beams is necessary. For this purpose it is offered to direct the relativistic electrons beam along the same orbit but towards (oppositely) to reacting particles beams.
This relativistic electron beam should compensate the positive space charge only partially and at the same time thanks to the magnetic attraction of combined three beams (three unidirectional currents) will compress the whole system in radial direction (pinch-effect). In fact pinch-effect will be provided thanks to the circumstance that in frame of reference connected with ions combined beam will charged negatively and for frame of reference connected with electrons – positively.
In the first approximation (not taking into consideration self-fields and influence of walls) the condition for beams for moving along the same equilibrium orbit is equality of gyroradiuses of particles.

Gyroradius can be calculated by the formula:

(1),
Where:
rg – gyroradius of particle
q – charge
B – induction of bending field
And equality of gyroradiuses for equally charged particles (e.g. deuterium, tritium and electron) means that their coherent motion momentums should be equal.

And e.g. for:
• Deuterium – 450keV
• Tritium – 300keV
• Electron – 40.6MeV
all momentums are equal to ~2.2*10-20 kg*m/s and at Bb=0.1T

rg=~1.4m

Deutrons 450keV and Tritons 300keV moving along the same axis at the same direction have center-of-mass collision energy ~30keV.
Such an energy provides rather high fusion cross section equal to ~1barn

G.I.Budker [1] says about achievability of order of magnitude of number density in such beams of 1026m-3 and even higher and beam’s radius of fractions of mm. Generally radial dimension of combined beam is a function of circulating currents, positive space charge neutralization level, coherent velocities of ions, relativistic factor γe and temperature. And varying with electron current for a given ion currents we can easily control the radius of combined beam.

For a given above sample of particles’ energies:
• γe=80.5 (relativistic factor of electrons in fixed frame of reference)
• γt=81.6 (relativistic factor of electrons in frame of reference connected with tritium)
• γd=82.2 (relativistic factor of electrons in frame of reference connected with deuterium)
And if nd=nt=ni/2, condition of pinch (excess of magnetic attraction forces on space charge repulse forces) will be:

ne>1/3355ni

So, the combined beam may be dramatically non-neutral and nevertheless suffering pinching. And this circumstance would be salutary for energy balance.

Injection challenge
Injection into vacuum chamber of very high current beams is a challenge. As the currents of thousands Amperes order for electron beam and tens/hundred thousand Amperes for ions are required. And such beams are space charge dominated.
But induction electron accelerators (Induction Linacs) produce rather high quality beams (energy spread <1%) and, so, having narrow phase volume (space), radius of vacuum chamber would have 0.5-2m order, while electron beam’s radius before injection – ~0.15m and electrons will be high relativistic 40.6MeV (γe=80.5, repulse forces reduce by factor of 1/γ2).
And commonly the injection of intense relativistic electron beams is well developed in number of laboratories [3] Fig. 1
And if we would inject firstly the electron beam and that then will totally fill the whole circumference (along axis) of chamber, the rather deep potential well for positively charged particles will be created, the depth of which is equal to [2]:

W=ve(1+2ln(R/Re)mec2 (2),

Where:
ve – Budker’s parameter ve = Ne2/m0c2 N-linear density (for Ie=4kA ve=0.235)
R – radius of vacuum chamber
Re – radius of electron beam
And for Ie=4kA, R=0.75m, Re=0.113m (je=10A/cm2)

W=1.123*mec2=574keV

And 574keV is rather enough depth for effective injecting into the same space ions producing by ion diodes even despite the fact that they have high energy spread and, so, big phase space.
Energies of ions:
Deuterium – 450keV
Tritium – 300keV

[Joseph Chikva]

Injectors
For electron injection it is more suitable to use Induction Linear Accelerators (Induction Linacs) producing:
• currents of kilo-amperes orders (10000 A by ATA accelerator [7])
• particles energies up to 50 MeV (with the spread <1% [7])
• pulse duration – 50 ns -1.2 μs
These parameters allow the effective injection of electron beams into the chamber with reasonable radial dimension (up to 2 m for modern TOKAMAKs)

For ions – the Ion Diodes or combination of Ion Diodes with additional Inductive Voltage Adders would be more suitable.
As:
• Ion Diodes produce currents up to mega-Amperes orders
• Energies of particles – up to several MeV (several hundreds keV are more common)
• Pulse duration – 50 ns – several μs
But energy spread produced by Ion Diodes is rather high and, so, big phase space.
From the one side wide spread would be useful for avoiding of some types of instabilities (e.g. two-stream instability) but from another – it makes more difficulties for injections. But as has been showed above, if electron beam would be injected before ions, that creates enough potential well for further injection of ions. Combination of Ion Diodes with Inductive Voltage Adders also dramatically reduces spread.

To apply the axial (toroidal) accelerating electric field.
If considering elastic collision of two particles moving at the same direction with different velocities, faster moving particle will transfer some momentum (and corresponding energy) to slower one, thus accelerating that and decelerating itself.
For the case when slower particle has bigger mass [1], [4]:

ΔE=γ2β2mc2 Θ/2
(3)
Δp= ΔE/v,

Where:
γ – relativistic factor of faster particle in the frame connected with slower
β – vrelative/c (vrelative – relative velocity of two particles)
m – mass of faster particle
Θ – scattering angle

And for interesting for us case average energy loss of faster moving Deuteron per each elastic collision (scattering event):

ΔE=10.9eV (corresponds to Θ=0.85 deg)
And taking into account that ratio between scattering and fusion cross sections differs on about 4 orders of magnitude, we should wait that:
• Deuteron 450keV decelerates to ~340keV
• Triton 300keV accelerates to ~410keV
before they fuse.
Naturally, mentioned above kinetic energies do not provide collision energy sufficient for fusion (not less than 10keV in center-of-mass frame)

And for this reason it is offered to apply along the axis the electric field accelerating particles in a manner similar to TOKAMAK in which that firstly breakdowns gas, ionizing that and drives the current.

TOKAMAK needs comparatively high intensity of electric field initially (up to 100 V/m when gas breakdown goes) but then by growth of plasma conductivity required intensity should be much lower (typical value of loop voltage – from fraction of Volt to 1 Volt which corresponds to 0.5V/m of intensity and even lower). Nevertheless due to high conductivity of hot plasma this voltage drives mega-Amperes order current.

For estimation of required intensity of electric field let us admit that:
• number density of pinched combined beam – 1023 m-3
• required confinement time in this case – 10-3 sec
And in this time the electric field of 50 V/m intensity will give to deuterium additional energy ~387keV and to tritium – ~240keV

And as result after the lapse of offered cycle will have:
• Deuteron 450keV accelerates to ~727keV
• Triton 300keV accelerates to ~650keV
that provides collision energy in center-of-mass frame

21.6keV (quite sufficient for fusion)

Here we should also to notice that particles from the beginning having equal gyroradiuses as result of described phenomena gain the certain mismatch from equilibrium momentums (about 18%) but also we have described that attraction of three unidirectional currents creates enough potential well confining them together.
According data provided by Stallatron (high current Betatron with additional Stellarator type windings) developers [5] such a scheme allows mismatch of energies up to 50% from equilibrium.

Requirements on axial electric field
For creation of axial electric field if we would use iron core transformer made of permendur (saturation limit 2.5 T), circumference of toroidal chamber L=15 m, inner area available for core S=20 m2 , mentioned above electric field E=50 V/m intensity can be kept in:
Bmin= – 2.4 T
Bmax= 2.4 T
Loop voltage :
Vloop=LE

t= S(Bmax-Bmin)/LE=0.128 sec = 128 milliseconds

So, after 1 millisecond there is enough reserve to pass then on lower intensity (~0.5 V/m) using in TOKAMAK mode with hot plasma.
At once after injection from the walls with the help of corresponding valves to puff into the vacuum chamber the gas consisting the fusion fuel components until filling the chamber up to desired pressure.
It is offered to use several gas-puff valves divided along circumference of reactor in regular intervals and to open them at certain moment puffing the certain quantity of gas: e.g. equal (by volume) mix of deuterium and tritium gases.
Already being there halo-layer will ionize that gas and then generate the current similarly to that how current is generated in so called Advanced TOKAMAKs (H-mode – beam driven current) and rise the temperature until thermonuclear temperature (higher than 10keV)
As the energy of halo-layer is in more convenient for energy transfer form – fast moving ions, energy of those ions 3.5MeV + energy corresponding to velocity of center-of-mass frame (2.63*106 m/s in considering here case) and that energy will be absorbed by cold gas within a few milliseconds increasing its temperature to desired value (10 keV and higher)

[Joseph Chikva]

At once after injection in regions free from axial magnetic field to apply such a field similar to that is applied in TOKAMAK reactors
Injection of charged particles across force lines of magnetic field is impossible. So, initially there should not be an axial/toroidal magnetic field at least near injection points.
But axial field is necessary for further confinement of hot plasma (that is the one of the main components of TOKAMAK confinement concept)
And there are some methods of fast creation of axial fields and then keeping them at constant value during certain period.
For example to use two coils: so called “fast coil” being lower in diameter, having lower inductance but conducting very high current. Such a coil may create short pulse magnetic field, while larger but more inductive coil’s field will rise slower but for longer time period till the end of necessity of confinement.

Conclusions

In present day’s magnetic confinement experimental fusion reactors the heating process of plasma goes too long time and during that inevitably causing the particle losses and radiation losses thus complicating ignition. Proposing Method allows more effective heating of plasma (more energy in less time period) and on base of the Method right now it is possible to build self-sustaining fusion reactor capable to produce net power.

Brief Description of the Drawings
• Fig. 1 – the scheme how plasma is heated in existing TOKAMAKs
• Fig. 2 – the scheme of injection of intense electron beam into the elongated by the racetracks toroidal chamber [3]
• Fig. 3 – the sample of possible embodiment of proposing plasma creation Method
• Fig. 4 – schematic of TOKAMAK’s field configuration

References:
1. Г.И. Будкер, Стабилизированный релятивистский элетронный пучок, Собрание трудов, Наука, 1982, стр. 208
2. Г.И. Будкер, Термоядерные реакции в потенциальной яме отрицательного заряда, Собрание трудов, Наука, 1982, стр. 147
3. Stanley Humphries, Jr., Charge Particle Beam, 1990, John Wiley and Sons
4. L.D.Landau and E.M. Lifshitz, Course of Theoretical Physics, vol. 1, Mechanics
5. C. W. ROBERSON & coauthors, The Stellatron Accelerator, Particle Accelerators, 1985, Vol. 17, pp. 79-107
6. Ben Dudson, Heating and current drive, Department of Physics, University of York, Heslington, 2011
7. L. L. REGINATO & ATA staff, THE ADVANCED TEST ACCELERATOR (ATA): A 50-MeV,’ 10-kA INDUCTION LINAC, 19S3 MARCH 21-23, 1983, PARTICLE ACCELERATOR CONFERENCE, SANTA FE, NEW MEXICO
8. Hansjoachim Bluhm, Pulsed Power Systems: Principles and Applications, 2006
9. Ronald C. Davidson & coauthors, Effects of a solenoidal focusing field on the electron–ion two-stream instability in high-intensity ion beams, Received 1 December 2000, Communicated by M. Porkolab. Available online 21 June 2001
10. Ronald C. Davidson & coauthors, Stabilizing influence of axial momentum spread on the two-stream instability in intense heavy ion beams, Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA, Available online 31 May 2001

[ikanreed]

That’s a neat idea, and some of the details go a bit above my head. I hope you have a better venue than a forum for sharing that idea.

[Joseph Chikva]

Thank you very much.
Certainly, I have some contacts with research institutions and also have sent to some Governmental organizations.
Last year I was invited at 53rd Annual Meeting of the APS Division of Plasma Physics http://meetings.aps.org/Meeting/DPP11/Event/153438 and 38th Conference on Plasma Physics of European Physical Society http://www-fusion-magnetique.cea.fr/eps2011/pages/postdeadline/index.html where I was going to make public only part of this idea.
Unfortunately I could not take participation in those events.
But am going to do that next year and have already received some invitations.
Due to limited validity of patents (20 years for Method and 10 years on Useful Device) I decided not to file patent application as I do not believe in fast financing opportunity, all the more if to take into consideration that such accelerators, magnet systems, vacuum chamber, etc. are rather costly and significant time period is required for design and commissioning.
Best regards,
Joseph

[Author]

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