Cyclic Fusion Reactor. Colliding Beams.

[Joseph Chikva]

Recently I have placed here the new - viable by my opinion Concept how to produce fusion.

By some reasons I have decided not to file the patent application and so for discussing now I am placing here the description of Cyclic Reactor on base of that Concept.

Ioseb (Joseph) Chikvashvili
________________________________________________________

Author: Ioseb Chikvashvili
?????????????????????????
Tbilisi, Georgia
Phone:
+ (995 32) ???????????????
+ (995 97) ???????????????

Invention

Cyclic Fusion Reactor Using Coaxial Passing Through Each Other Self-focusing Colliding Beams


Abstract

In the simplest embodiment the proposed Cyclic Fusion Reactor includes: betatron type device (circular store of externally injected particles – induction accelerator, e.g. FFAG, Stellatron, induction synchrotron, etc.), pulse high-current relativistic electron injector, pulse high-current slower ion injector, pulse high-current faster ion injector and reaction products extractor.
All 3 (three) types of injectors produce the beams of particles with a such parity of kinetic energies and corresponding momentums (depending on using particles’ mass-to-charge ratio) and have relative to betatron type device a such spatial arrangement that allow particles to move on a common equilibrium betatron orbit 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 moves oppositely to ions thus allowing to combined beam the self-focusing (pinch-effect) capability thanks to the only partial compensation of reacting particles’ positive space charge and also to the magnetic attraction of all 3 (three) unidirectional currents. Circular accelerating electric field of betatron type device compensates occurring together with fusion the: alignment of velocities of reacting particles and also energy losses of electrons via braking radiation (Bremsstrahlung). Reaction products extractor allows the extraction of only charge particles – fusion products while uncharged fusion products – neutrons escape the reaction zone independently.


Claims

1. A device for generating fusion reactions, the device comprising:
1. betatron type device
2. at least 1 (one) pulse high-current relativistic electron injector
3. at least 1 (one) pulse high-current slower ion injector
4. at least 1 (one) pulse high-current faster ion injector
5. at least 1 (one) reaction products extractor

2. The device of claim 1, wherein betatron type device (circular particles store – induction accelerator, e.g. FFAG, stellatron, induction synchrotron, etc.) configured to store and accelerate 3 (three) different particles beams at the certain common equilibrium orbit.
• 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 arranged (coherent) motion velocities.
So, one faster ion beam should transit through another slower ion beam and their relative speed (velocity) should be sufficient for providing for 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.
• Except of target fusion events at the expense of elastic collisions (multiple scatterings) basically of ions (ion-ion Coulomb scattering) in a combined beam inevitably the following phenomena will be observed: acceleration of slower ions with decelerating of faster ions (alignment of arrange velocities of reacting nuclei reducing the collision energy between them) and also the growth of temperature (“thermalization”).
Nature of thermalization:
After each scattering event automatically thanks to the very strong poloidal self-magnetic field the scattered nucleus will return back to the axis transferring only the part of radial momentum acquiring as result of scattering mostly to the electron gas. Then the thermal energy acquired by the electron gas via collective electron-ion interaction partly will be transferred to the ion gas (both ion fractions) thus increasing also ion temperature in combined beam and partly will be dissipated at the expense of braking radiation (Bremsstrahlung). So, a certain thermal equilibrium will occur.
• And an externally applied to the combined beam induction longitudinal (circular) electric field created by the betatron type device thanks to its varying (time-dependent) magnetic field will compensate the alignment of velocities of nuclei beams and also will compensate the energy losses (radiant losses) of focusing electrons.
The compensation of the alignment of velocities will be possible in case if in faster moving ion beams the ions having higher rate of acceleration will be used.
For example: in Deuterium+Tritium reaction case in faster moving ion beam Deuterium nuclei should be used and in case of aneutronic D+He3 reaction – He3 nuclei.

The following conditions should be satisfied for betatron type device 1:
• At the injection moment all three types of operated particles should have the charge-momentum ratio allowing them to be catch and then accelerated at a single common equilibrium betatron orbit.
For example: in case of deuterium-tritium reaction there needed that all three types of particles will have an equal momentums, and in case of aneutronic Deuterium+He3 reaction the momentum of He3 particle should be 2 times more than Deuterium’s and electron’s momentums.
• Collision energy in center-of-mass frame of two different types of nuclei should be sufficient for overcoming of Coulomb barrier and executing fusion at high enough cross-section.

Samples
Deuterium+Tritium Reaction
• Deuterium – 300 keV
• Tritium – 200 keV
• Center-of-mass collision energy – 20.2 keV
• Reaction cross section – 0.4 barn
• Ions’ relative velocity – 1.8*10^6 m/s
• Electron – 33 MeV
• Relativistic factor of electrons – 65.6

Deuterium+Tritium Reaction
• Deuterium – 960 keV
• Tritium – 640 keV
• Center-of-mass collision energy – 64 keV
• Reaction cross section – 5 barn
• Ions’ relative velocity – 3.2*10^6 m/s
• Electron – 60 MeV
• Relativistic factor of electrons – 118.4

Deuterium+He3 Reaction
• Deuterium – 1.71 MeV
• He3 – 4.58 MeV
• Center-of-mass collision energy – 115.7 keV
• Reaction cross section – ~0.2 barn
• Ions’ relative velocity – 4.3*10^6 m/s
• Electron – 80 MeV
• Relativistic factor of electrons – 157.6

3. The device of claim 2, wherein pulse high-current relativistic electron injector. Injects focusing relativistic electron to the equilibrium orbit of betatron type device 1.
There are several types of pulse charged particles accelerators that may be used. But it would be preferable to use the linear induction accelerators due to their ability to produce very high currents (up to tens thousand amperes) and at the same time high current densities as well. Also due to their high pulse repeatability (up to 10 Hz)

4. The device of claim 3, wherein pulse high-current slower ion injector. Injects slower moving ions to the equilibrium orbit of betatron type device 1.

5. The device of claim 4, wherein pulse high-current faster ion injector. Injects faster moving ions to equilibrium orbit of betatron type device 1.

6. The device of claim 5, wherein reaction products extractor. Configured to extract the charged particles remaining as a reaction’s products from betatron type device 1 thus freeing the space for a new production cycle. (In case e.g. deuterium-tritium reaction neutrons will escape the reaction zone from themselves while alpha-particles will remain in reaction zone and should to be extracted)
There is a set of various possible variants (options) of reaction products extractor’s design. Therefore it would be expedient that the detailed design of reaction products extractor will be the subject of the separate patent application.

Field of the Invention

The invention relates generally to the field of plasma physics, and, in particular, to methods and apparatus for confining plasma. Plasma confinement is particularly of interest for the purpose of enabling a nuclear fusion reaction.

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, if the required kinetic energy would be provided by heating of plasma, the fusion rate can be appreciable if the temperature is at least of the order of 10^4eV – 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 30keV and 100keV.
Also, unlike the methods using high-thermal plasma in which kinetic energy is provided to nuclei by heating, some other methods use coherent motion kinetic energy of particles for overcoming the Coulomb barrier.
For example, Dr. Norman Rostoker’s approach of colliding beams.

For execution of controlled fusion for commercial purposes the fusion device should provide the following:
• to provide enough kinetic energy to reacting nuclei
• to provide enough confinement time (duration) allowing to fuse for enough quantity of nuclei (fusion energy yield should exceed the energy expenses)

The proposed fusion device unlike to all other approaches uses the coherent motion of two different types of nuclei beams moving in orthogonal magnetic field, directed at the common equilibrium orbit and moving in the same direction passing through each other with different velocities. So, nuclei from fast moving beam should catch up and collide the nuclei from slower moving beam.
And this is possible if both types of reacting nuclei will have the same gyroradiuses.

(1)
where:
• p – coherent momentum of particle
• q – charge of particle
• B – magnetic induction
For note: The formula doesn't consider self-magnetic field of a beam but surely applicable in considered case.

Also the second requirement is that the velocities’ difference between nuclei of different beams should be high enough for providing to faster moving nuclei enough for fusion collision energy in center-of-mass frame.

For example, if we use D-T reaction we can direct at the same orbit 300keV Deuterium and 200keV Tritium beams. As in this case both types of equally charged nuclei will also have the same momentums and subsequently will have the same gyroradiuses.
Center-of-mass collision energy in this case will be equal to ~20.2keV providing fusion cross section of about 0.4 barn.
For note: D-T reaction has a peak equal to 5 barn at ~64keV center-of-mass energy

On base of today’s level of technology it is possible to create pulse ions beams with mentioned above energies providing currents of tens thousands Amperes. Such accelerators are used for example in beam driven inertial confinement experiments.
Pulse repeatability of modern linear induction particles accelerators (induction linacs) has an order of magnitude 10Hz.
But the technically feasible current density of beams produced by those accelerators does not exceed 10-20 A/cm2 (For particle’s energies of hundreds keV the mentioned current density corresponds to 10^16-10^17m-3 number density)
So, without focusing the very low fusion power density is possible to achieve. All the more without focusing the non-neutralized positive space charge together with inevitably occurring ion-ion scattering events will expand beams in radial direction.

And for focusing it is offered to direct at the same equilibrium orbit but oppositely to ions’ direction the relativistic electron beam with the energy corresponding to the same gyroradius.
As it is well-known in relativistic beams the repulsive forces between particles are reduced by 1/γ2.
And relativistic electrons should compensate the positive space charge of reacting nuclei only partially while the magnetic attraction of three unidirectional currents will compress combined beam in radial direction.
In fact for the frame of reference connected with ions combined beam will be charged negatively and for electron’s frame of reference – positively. So, reacting nuclei in their frame of reference will be in negative potential well and electrons in their frame – in positive potential well.
And thanks to mentioned above the required for focusing electron current should be much lower than for ions.

For example: In the considering here parameters: 300keV for Deuterium and 200keV Tritium we need about 33MeV (high-relativistic – γ=~65.6) electron beam for providing to electrons the possibility of moving at the same orbit.
For the frame of reference connected with Deuterium beam this corresponds to electron’s relativistic factor equal to 66.7 and for Tritium – 66.3)
And for effective pinch the required current of electron beam should be more than only ~1/52.6 of current of Tritium beam and ~1/80 of Deuterium.
And from these reasonings we can accept the ratio between electron and Tritium and Deuterium currents equal to 1/50 and 1/75 correspondently.

The raw estimation of required energy that should to be put into the beams specified on a single fusion event (initial energy consumption of a single fusion event)
In case if only 80% of nuclei will react initially we should spend per one fusion event:

(300keV+1/75*33MeV+200keV+1/50*33MeV)/0.8=2MeV

Except of target fusion events in a combined beam at the expense of elastic collisions (multiple scatterings) basically of ions (ion-ion Coulomb scattering) inevitably the following phenomena will be observed: acceleration of slower ions with decelerating of faster ions (alignment of arrange velocities of reacting nuclei reducing the collision energy between them) and also the growth of temperature (“thermalization”).

Nature of “thermalization”:
After each scattering event thanks to the very strong poloidal self-magnetic field the scattered nucleus automatically will return back to the axis transferring only the part of that radial momentum acquiring as result of scattering mostly to the electrons gas. Then the thermal energy acquired by the electron gas via collective electron-ion interaction partly will be transferred to the ion gas (both ion fractions) thus increasing also ion temperature in combined beam and partly will be dissipated at the expense of braking radiation (Bremsstrahlung). So, a certain thermal equilibrium will occur.

The alignment of arrange velocities will decrease the fusion cross section simultaneously increasing the scattering cross section.
But if we will use an externally applied induced longitudinal (circular) electric field created by varying (time-dependent) magnetic field we can easily compensate the alignment of velocities as faster moving ions in proposed reactions (Deuterium for D-T nuclei pair and He3 for D-He3 pair) at the same time have also a higher rate of acceleration in the same electric field.

And logically we went to the design of betatron type device producing the varying (time-dependent) magnetic field for holding the externally injected particles on a common equilibrium orbit and simultaneously creating the circular electric field for their acceleration.
And modern betatrons: (Fixed-Field Alternating Gradient accelerator (FFAG), betatron with additional Stellarator windings (Stellatron), induction synchrotron (IS), etc.) can provide currents of thousand Amperes orders of magnitude with high repeatability.
Note: mentioned currents are provided in case of non-neutralized space charge, but proposed Method provides the ability of neutralization. So, no space charge current limitation!

The creation and further maintenance process of inducing an accelerating electric field (its loading with the proposed beams) will connect with additional energy expenses.

The raw estimation of energy consumptions during namely fusion process (pinch, accelerating particles for compensation of alignment of ions’ velocities and also for compensation of electron radiation losses) specified on a single fusion event – 0.7MeV.

So, the raw estimation of total energy consumption specified per a single fusion event
2MeV+0.7MeV=2.7MeV

And taking into consideration the efficiency of beams generation and also the efficiency of their further maintenance – ~35%, we will have the total energy consumption specified per a single fusion event equal to:
~7.72MeV

From the other side from each fusion event we will have:
• one 14.1MeV neutron
• about 0.5MeV of X-ray radiation
• 1.25*4.8MeV=6MeV thermal energy via (n+Li6) reaction (where “1.25” is a Tritium breeding coefficient)
So, from each event total energy of 20.6MeV should be converted into the electricity via thermal cycle (efficiency ~40%).
And the energy gained from a single fusion event by thermal cycle:

8.24MeV

8.24Mev of yield vs. 7.72MeV of expences

Or in the other words considering the real efficiency of using in Reactor energy conversion cycles even only the thermal cycle can provide breakeven!
For example, Lawson criterion written for TOKAMAK and other experiments using the magnetically confined thermal plasma does not consider efficiency of energy conversion and by this reason seems as too optimistic. Nevertheless even that optimistic criterion in mentioned experiments was not satisfied till now.

Besides the energy gained by thermal cycle the proposed Reactor can gain also the energy of charged particles as well:
• He4 – 3.5MeV
• electron – some part from initial 33MeV
• some part of energy initially pumped into ions acceleration 0.5MeV
And that energy can be gained via Direct Energy Conversion process with higher than in thermal cycle efficiency – not less than 50%.

Conclusions

The invention provides the opportunity to produce net power by the way of executing controlled nuclear fusion reaction using present day technologies and materials (or a reasonable extrapolation of those).

[chrismb]

So, again I ask, what magnetic field do you need so as to cause a 1.71MeV deuteron to undergo a gyration within the geometry of your device so it is not lost?

[Joseph Chikva]

So, again I ask, what magnetic field do you need so as to cause a 1.71MeV deuteron to undergo a gyration within the geometry of your device so it is not lost?

Chris, before asking firstly you should learn something more on magnetism. Then to put question correctly.
As I have not 1.71MeV deuterons.

[chrismb]

Then your description above is unintellgible because that is one of the examples you have given.

[Joseph Chikva]

So, again I ask, what magnetic field do you need so as to cause a 1.71MeV deuteron to undergo a gyration within the geometry of your device so it is not lost?

Pardon, you are talking about this sample:

Deuterium+He3 Reaction
• Deuterium – 1.71 MeV
• He3 – 4.58 MeV
• Center-of-mass collision energy – 115.7 keV
• Reaction cross section – ~0.2 barn
• Ions’ relative velocity – 4.3*10^6 m/s
• Electron – 80 MeV
• Relativistic factor of electrons – 157.6

I need the same mag field for keeping at the common equilibrium orbit three types of particles:
• Deuterium – 1.71 MeV
• He3 – 4.58 MeV
• Electron – 80 MeV
As at these energies they have the same gyroradiuses.
For note: mag field in betatrons are not fixed but time-dependent. And there are betatrons for 200MeV electrons

[chrismb]

• Deuterium – 1.71 MeV
• He3 – 4.58 MeV
• Electron – 80 MeV
As at these energies they have the same gyroradiuses.

I doubt it!!! But moving on from some arithmetic errors we can look at again:

I do not understand why you cannot simply interpret the question as meaning the maximum field, in a time-variant system, but I shall ask alternately; what is the maximum magnetic field a 1.71MeV deuteron will ever experience in your device?

[Joseph Chikva]

I doubt it!!! But moving on from some arithmetic errors we can look at again:

I do not understand why you cannot simply interpret the question as meaning the maximum field, in a time-variant system, but I shall ask alternately; what is the maximum magnetic field a 1.71MeV deuteron will ever experience in your device?

If you doubt - that's your problem.
But Deuteron at 1.71MeV and electron at 80MeV have the same momentums equal to ~4.3E-20 kg*m/s and He3 at 4.58 MeV has 2 times more - ~8.6E-20 kg*m/s.
Bending mag field in betatrons has an order of magnitude about 0.2-0.4 Tesla.
Formula of gyroradius (if not considering self-magnetic field of beam):
R=p/(q*B)
Where:
• p-momentum
• q-particle's charge (equal to ~1,6E-19 for Deuteron and electron and ~3,2E-19 for He3)
• B-as mentioned

[chrismb]

Ah!! Numbers! [Mon Dieu!]

OK, I withdraw my doubt on the arithmetic.

So now we contend with the question of scattered particles. How does a scattered particle return to the beamline. Can you provide a diagram of the behaviour of these beam ions undergoing scattering?

I'm also curious why you pitched your 'patent text' as being "to methods and apparatus for confining plasma". So is this an ion beam method, a beam-into-plasma method, or a way of exciting a plasma? Or is it a loose use of the word 'plasma' incorporating all these things.

[Joseph Chikva]

Ah!! Numbers! [Mon Dieu!]

OK, I withdraw my doubt on the arithmetic.

So now we contend with the question of scattered particles. How does a scattered particle return to the beamline. Can you provide a diagram of the behaviour of these beam ions undergoing scattering?

I'm also curious why you pitched your 'patent text' as being "to methods and apparatus for confining plasma". So is this an ion beam method, a beam-into-plasma method, or a way of exciting a plasma? Or is it a loose use of the word 'plasma' incorporating all these things.

Regarding scattered particles I can answer the same as earler: The beam creates the poloidal self-magnetic field and the radial momentum got by particle and accordingly the radial velocity and so creates the Lorenz force returning particle back to the axis.
In this process scattered particle losses only the part of its radial momentum has been got via scattering by passing that lost part mainly to electron gas.

Regarding terminology, combined beam can be considered as non-neutral plasma. And there are a few teams around the world working in this area.
E.g. http://nonneutral.pppl.gov/

[chrismb]

Within the description you've given, each time an ion is scattered then it would 'hop' into a different gyro-orbit, displaced from the first. This is just typical gyro-hopping behaviour in any plasma device. What mechanism brings it back onto the same gyro-orbit, whilst also putting more energy into it so it doesn't drop its velocity and so begin a process of thermalisation?

[Joseph Chikva]

Within the description you've given, each time an ion is scattered then it would 'hop' into a different gyro-orbit, displaced from the first. This is just typical gyro-hopping behaviour in any plasma device.

Again you make statements confirmed with nothing. Betatrons and especially FFAG betatrons and Stellatrons are stable against mismatch of un-equilibrium energies.
You can for example see here: http://cdsweb.cern.ch/record/1108024/files/p79.pdf on page 81 somewhere after formula

By adding a stellarator field to a cyclic accelerator, a strong-focusing system is obtained that can sustain high currents and large mismatch between particle energy and vertical field

Somewhere else is written that stellatron runs well even if that mismatch reaches 50%

What mechanism brings it back onto the same gyro-orbit, whilst also putting more energy into it so it doesn't drop its velocity and so begin a process of thermalisation?

Thermalization and braking radiation begin together with beginning of pinch. But thermal equilibria then will occur. Energy lossing preventing mechanism is acceleration in betatron's induction electric field.
In which faster ions have higher rate of acceleration.

[chrismb]

Within the description you've given, each time an ion is scattered then it would 'hop' into a different gyro-orbit, displaced from the first. This is just typical gyro-hopping behaviour in any plasma device.

Again you make statements confirmed with nothing. Betatrons and especially FFAG betatrons and Stellatrons are stable against mismatch of un-equilibrium energies.
You can for example see here: http://cdsweb.cern.ch/record/1108024/files/p79.pdf on page 81

An interesting paper, but again I do not think you comprehend the paper. This is describing a non-collisional electron device. For such a device, collisional behaviour is entirely lossy and is to be avoided. Collisions would destabilise the orbits [in the manner I summarise]. Your device you need high collisionality.

[Joseph Chikva]

An interesting paper, but again I do not think you comprehend the paper. This is describing a non-collisional electron device. For such a device, collisional behaviour is entirely lossy and is to be avoided. Collisions would destabilise the orbits [in the manner I summarise]. Your device you need high collisionality.

I understand more than you guess.

For example, I know the betatron theory in which the behavior of the particle having energy distinct from the equilibrium is described.
Or by any reasons (e.g. collisions) got into an orbit not too far from the equilibrium.
And there are the focusing forces in betatron returning the particle into an equilibrium orbit.
Particles in betatron are absolutely stable.

Above I told about betatron focusing (external focusing) to which we also should add combined beam’s self-focusing capability thanks to self-magnetic field.

[chrismb]

The 'focussing' is NOT re-focussing of scattered particles, it is focussing of particles that have experienced, or are experiencing, small perturbations about the equilibrium position.

[Joseph Chikva]

The 'focussing' is NOT re-focussing of scattered particles, it is focussing of particles that have experienced, or are experiencing, small perturbations about the equilibrium position.

Yes, you are absolutely right that focusing is not re-focusing.
What is small perturbation without fixing the reason why they occur?
May scatterings at small angles be considered as small perturbations? And so on.