The Draft of Poster of New Fusion Concept

[Joseph Chikva]

The Draft of Poster of New Fusion Concept that I am going to represent at 53rd Annual Meeting organized by Plasma Physics Division of American Physical Society (attached file)
Without drawings yet but I will complete drawings till mentioned event.

Edited 09/26/2011: I have uploaded the final edition of Poster with pics (only main body – left side, right side consisting of four pics and text about instabilities, has more than MB size and can not be uploaded here)

[jamesr]

A couple of points…

Although you mention briefly ion scattering, I don’t think you appreciate the stability (or lack thereof) of the conditions you are trying to achieve.

You will get wave-particle interactions, coupling to all sorts of kink and ballooning modes. The plasma instabilities will grow on a much faster time-scale than can be controlled, and hit the walls within a microsecond.

A linear design would have to be hundreds of kilometres long, and a ‘cyclic’ design is essentially a Tokamak, ie governed by all the same stability criteria of q-profile, Troyon limit etc.

Also the acceleration of ion/electron beams to high energies is not efficient enough – you will never get the Q number you claim.

[Joseph Chikva]

jamesr wrote: A couple of points…

Although you mention briefly ion scattering, I don’t think you appreciate the stability (or lack thereof) of the conditions you are trying to achieve.

You will get wave-particle interactions, coupling to all sorts of kink and ballooning modes. The plasma instabilities will grow on a much faster time-scale than can be controlled, and hit the walls within a microsecond.

A linear design would have to be hundreds of kilometres long, and a ‘cyclic’ design is essentially a Tokamak, ie governed by all the same stability criteria of q-profile, Troyon limit etc.

Also the acceleration of ion/electron beams to high energies is not efficient enough – you will never get the Q number you claim.

Claimed Energy Gain Factor is defined like to other experiments – without considering of efficiency of energy conversion cycles.
This number only shows how wide area we have.
For example, if considering real efficiency of cycles involved in TOKAMAKs, net energy will go from there only after ~600s of confinement.

Acceleration of electrons by induction linacs – 35% effeciency (produces flat-top pulse using 100-200 inductive cavities)
Acceleration of ions by gas-puff magnetically insulated ion diodes – 70% efficiency (produces wide spread bell-like pulse)
We can accelerate ions by diode to lower energy. e.g. 150keV adding then e.g. one induction cavity (Inductive Voltage Adder) on 150keV for Tritons and two Adders for Deuterons. This trick would dramatically reduce the spread but at the same time also would a little bit reduce efficiency as well.
In any case acceleration efficiency will not be less 35%
So, energy has to be pumped in to the beams and specified per each occurred fusion event would not be more than:
2.26MeV/0.35=6.46MeV

From the other side using only thermal cycle with 40% efficiency we will have:
19.62MeV*0.4=7.8MeV

Or 1.36MeV from each event gained from thermal cycle

Plus energy from direct energy converter. Here we also should consider that energy initially pumped into the beams does not lose but can be recovered with some efficiency.

Regarding instabilities:
For already at least 30 years people learned up how to fight with kink and sausage instabilities in Z-pinch and TOKAMAKs.
Longitudinal mag field is very effective against short wave instabilities. Long wave kink instability has also long development time and, so, that can be eliminated by means of feedback and electrostatic quadrupole. This trick is also proposed for Heavy Ions Fusion experiment.

Balloon effect is not issue for proposed method at all.

I mentioned scattering briefly because that is well known for auditory for whom that Poster is prepared.

I also mentioned G.I. Budker and his “Stabilized Electron Beam” paper in wich is claimed that Bremsstrahlung in proposed formations is very effective against most types of instabilities. As electrons moving in very strong self-magnetic field lose not only axial coherent energy but also radial energy as well damping effectively all types of waves.
http://resources.metapress.com/pdf-preview.axd?code=r6570k3897767838&size=largest

Strong magnetic self-focusing causes characteristic electromagnetic radiation which tends to damp out transverse electron oscillations. If certain other conditions are also satisfied, this effect causes the beam to contract into a thin thread-like structure with enormous electric and magnetic field at the surface and which is apparently a stable and long-lived configuration.

So, we have two stabilizing factors:
• Longitudinal (toroidal) mag field
• Bremsstrahlung

And taking into account that confinement scheme is very similar to TOKAMAKs and we have temperatures on orders of magnitude lower than in TOKAMAKs, we can wait that feasible confinement time will be at least not less than in TOKAMAKs (seconds order). And we need only millisecond order confinement time.

Linear design needs not hundreds but a few kilometers length. Comparing with e.g. LHC’s circumference this is not so bad. As linear design has not some limitations of cyclic.

[delt0r]

I see a lot of assertions and no math. In fact i see quite a bit of misunderstanding of fundamental plasma physics. The ion “scattering” cross section is generally defined as the 90Deg angle scattering. It is many many times higher than the fusion cross section, they do not stay confined. No matter what you do with one beam compared to another, it physically identical to having one set of ions stationary and the other colliding with them (your reference frame just moves with one beam–the results are always the same), in this case they just scatter, and your densities are way too low for any real fusion. Unless you have some uber magic accelerator. In which case light ion ICF is totally easy. We have not solved kink and sausage instability without a theta field and hence low beta limits*. There are many more things wrong with the physics sorry (Just asserting that XXX instability is not an issue does not cut it). Also the English needs work. Even the title does not make much sense.

It should be noted that Lerner has *not* swept any known plasma instability under the carpet. He has and continues to address every possible issue in this regard. This is why he gets publications out while a lot of the IEC crowed do not.

*There is shear stabilized z pinch. However there was only a few experiments so far, and only one with high currents. Oh and the so called advanced mode Tokamak which is also shear stabilized IIRC, but then there is these pesky ELM.

[Joseph Chikva]

delt0r wrote: I see a lot of assertions and no math.

I see a lot of your wrong assertions and also no math

delt0r wrote: In fact i see quite a bit of misunderstanding of fundamental plasma physics. The ion “scattering” cross section is generally defined as the 90Deg angle scattering. It is many many times higher than the fusion cross section, they do not stay confined.

Please explain where I have defined only 90deg scattering, where I have showed that I do not know that scattering cross section is much higher than fusion cross section and also please explain what do you mean saying “they do not stay confined”.

delt0r wrote: No matter what you do with one beam compared to another, it physically identical to having one set of ions stationary and the other colliding with them (your reference frame just moves with one beam–the results are always the same), in this case they just scatter, and your densities are way too low for any real fusion.

It is not physically identical have you fixed cloud of charges or you have moving charges’ stream (current)! Please before discussing learn something more about magnetism. For the beginning e.g. from here: Magnetic Field of a Moving Charge http://academic.mu.edu/phys/matthysd/web004/l0220.htm FB/FE=v^2/c^2 and you are wrong saying “your reference frame just moves with one beam–the results are always the same”. Mag fields are not the same for different frames. And for your note we are talking about magnetic confinement concept.

delt0r wrote: Unless you have some uber magic accelerator. In which case light ion ICF is totally easy.

All quoted by me accelerators’ parameters are already achieved!
For example:
ATA electron accelerator producing 10’000A and 50MeV is already decommissioned by Lawrence Livermore Lab: http://www.osti.gov/bridge/servlets/purl/6333447-IdCL1y/6333447.pdf
Also,
100-200A/cm2 current density is absolutely not magic for magnetically insulated ion diodes: http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/22/087/22087074.pdf

delt0r wrote: We have not solved kink and sausage instability without a theta field and hence low beta limits*

Absolutely wrong. For at least 30 years kink and sausage instabilities and methods how to fight with them are described in any plasma physics books. As well as many other types of instabilities. May be you do not know about that.
If you mean “toroidal” saying “theta field”, yes, my concept like “modified betatron” needs one from the following: alternating gradient field or stellarator field or simple toroidal field. And yes, TOKAMAK has simple toroidal field and therefore low beta.

delt0r wrote: Also the English needs work. Even the title does not make much sense.

Sorry for bad English. But as I see that is not so bad. As even with your knowledge limitations you understood what I talk about.

delt0r wrote: It should be noted that Lerner has *not* swept any known plasma instability under the carpet. He has and continues to address every possible issue in this regard. This is why he gets publications out while a lot of the IEC crowed do not.

*There is shear stabilized z pinch. However there was only a few experiments so far, and only one with high currents. Oh and the so called advanced mode Tokamak which is also shear stabilized IIRC, but then there is these pesky ELM.

And finally. I don’t compete with Dr. Lerner. Let God grant him the health and all success. I only say that my concept is very similar to ТОКАМАК, temperature on orders of magnitude lesser, mag fields have the same order. On what confinement time can we expect? Not at least on the same? Not seconds order?

[jamesr]

I think delt0r and I were trying to be polite about the idea.

Confining a charged ion beam in a large aspect ratio ring is one thing. But once you introduce a second beam at a different velocity it will be unstable.
http://en.wikipedia.org/wiki/Two-stream_instability
Here is an animation – note the y axis is velocity, so you start with the beams being two lines at different y positions. Then through wave-particle interactions it goes unstable and you quickly get a mix in velocity space (this doesn’t require any large angle collisions).
http://www.youtube.com/watch?v=ZzJFvYVVWPw
This, with collisions, will settle down to a Maxwellian thermal equilibrium.

Also, if your two beams had a deltaE of 30keV this would be the approximate temperature they relax to. Given your ridiculously high estimate of density of 10^23m^-3 this would equate to a pressure of 4.7*10^8 Pa or 4700 atmospheres. I’ll leave you to figure out the magnetic field you need to contain that at a beta of less than 1.
Even if the pressure was highly anisotropic so the radial part was only a few percent of the total, the required toroidal field would be impossible to create on that scale.

[Joseph Chikva]

You are absolutely right worrying about two-stream instability. That is issue of given Concept.
But this type of instability is more critical for electron-electron streams interaction and less for electron-ion or ion-ion.

Applications of the two-stream instability to plasma heating involve high-power-density relativistic beams. We have found that the growth of the two-stream instability depends on changes in the axial velocity of beam particles. Because a relativistic beam travels near the speed of light variations of kinetic energy cause only small changes of axial velocity. Therefore, bunching takes place slowly for a relativistic beam.

Stanley Humphries, Jr., Charged Particle Beams, Originally published in1990 by John Wiley and Sons
Also:

Instability of relativistic electron beam with strong magnetic field Zhijing Liu, H. L. Berk and Xiantu He

http://www.springerlink.com/content/q61nq245w64h35p5/

Annotation

Stability criteria for a weak relativistic beam-plasma interaction in a strong magnetic field are found. Two beam modes occur,ω≈k zC andω≈k zC-ωc. The dispersion equation of electrostatic two-stream is exactly solved with analytical method.

Also:

Two-stream instability in the presence of longitudinal magnetic field, El-Labany, S. K.; El-Hanbaly, A. M.

http://adsabs.harvard.edu/abs/1989Ap&SS.153…75E

Abstract

A multiple scales perturbation theory has been applied to investigate the nonlinear behavior of beam-plasma system near a marginally stable state in the presence of longitudinal magnetic field. The perturbation method leads to a nonlinear Schroedinger equation for the finite amplitude. The coefficients of this equation show that only if the beam is compressed isothermally can there exist a range of wavenumbers for which stabilization might occur. The stable region increases with the applied magnetic field.

Commonly, strong longitudinal mag field, high relativistic factors, absence of electron-electron streams interaction and some consultations with very skilled experts allow me to be sure on this type of instability too.

In a given sample I have kinetic energy difference equal to 150keV, but center-of-mass collision energy is equal only to 30keV. Yes, this will create transverse momentums depending on impact parameter the value of which is probabilistic. But scattered particle will return back to the axis then oscillating around that. During oscillation only part of radial (transverse) momentums will be transferred to electron gas. Electron oscillations will be damped thanks to Bremsstrahlung. And certain thermal equilibrium will occur.

Mentioning your pressure estimation 4.7*10^8 Pa except number density you should also know temperature as well. And you do not. At least I did not say yet. Recall that Ohmic heating of plasma is more effective at low collision energies and less effective at high. And we initially will have high collision energy that should then be kept comparatively constant thanks to externally applied electric field.
We will have 444’000 Amperes of circulated current and combined beam’s diameter about 5mm. Before calculating of kinetic pressure can we calculate mag field yet? And its pressure?

[Joseph Chikva]

Additionally about the ways how to defend combined beam against two-stream instability:

Effects of a solenoidal focusing field on the electron–ion two-stream instability in high-intensity ion beams
Ronald C. Davidson, Han S. Uhm
http://www.sciencedirect.com/science/article/pii/S0375960101002456

Abstract
A rigid-beam model is used to investigate the influence of a solenoidal focusing field on the electron–ion two-stream instability that can occur in high-intensity ion beams when an (unwanted) component of background electrons is present. A relatively weak solenoidal magnetic field strongly constrains the transverse electron motion and can lead to a significant reduction in instability growth rate whenever ω2ce⪢2(nbeb/nee)ω2pe. Here, ωce=eB0/mec is the electron gyrofrequency, ωpe=(4πnee2/me)1/2 is the electron plasma frequency, and nb and ne are the ion and electron number densities.

Note#1: “solenoidal” means “longitudinal” for cylindrical beam and “toroidal” for cyclic beam. So, TOKAMAK like field configuration would be very useful.
Note#2: “relatively weak solenoidal magnetic field” means “relatively high beta” (unlike TOKAMAK)

[Joseph Chikva]

delt0r wrote: *There is shear stabilized z pinch. However there was only a few experiments so far, and only one with high currents.

Bellow are data of already achieved and not projected parameters:

Gas-puff Z-pinch
Current 0.5MA was really achived in 1988
http://mifti.com/yahoo_site_admin/assets/docs/JApplPhys_64_3831.305212637.pdf

Wire array Z-pinch (Z-machine by Sandia National Laboratory)
http://www.sandia.gov/z-machine/
Current tens MA

JET Joint European Torus
http://en.wikipedia.org/wiki/Joint_European_Torus
Current 3.2MA
Lifetime of plasma 20-60s (if to believe to Wiki – as I doubt, but fraction of second or seconds in any case)
Edited:
•Current 5 mega amperes http://www.jet.efda.org/jet/jets-main-features/
•Energy Confinement Time: (t) 4-6 seconds http://www.jet.efda.org/fusion-basics/conditions-for-a-fusion-reaction/

About kink and sausage instabilities
http://www.jp-petit.org/science/Z-machine/HAINES_juin_2011.pdf

The theoretical models available at that time, e.g. Kruskal and Schwarzchild [37], Tayler [38], were analytic and based on ideal magnetohydrodynamics (MHD), and showed that both sausage (m = 0) and kink (m = 1) modes could be present.
Whilst many researchers then added axial magnetic fields or, in toroidal discharges, a toroidal magnetic field component in order to find a more stable equilibrium, the price that is paid for this is that one is then limited to low density (n < 10^16 cm^−3) discharges and, for fusion also, large volume devices, because of the practical upper limit of magnetic field that can be produced by coils.

For note: n=10^16 cm^−3=10^22 m^-3
But TOKAMAKs as a rule have lower number density of 10^20 m^-3 order

[Joseph Chikva]

Here in this thread one of my posts is lost. I do not understand how. Or why?
As jamesr said:

Also, if your two beams had a deltaE of 30keV this would be the approximate temperature they relax to. Given your ridiculously high estimate of density of 10^23m^-3 this would equate to a pressure of 4.7*10^8 Pa or 4700 atmospheres. I’ll leave you to figure out the magnetic field you need to contain that at a beta of less than 1.

On which I have answered:

Mentioning your pressure estimation 4.7*10^8 Pa except number density you should also know temperature as well. And you do not. At least I did not say yet. Recall that Ohmic heating of plasma is more effective at low collision energies and less effective at high. And we initially will have high collision energy that should then be kept comparatively constant thanks to externally applied electric field.

then asking:

We will have 444’000 Amperes of circulated current and combined beam’s diameter about 5mm. Before calculating of kinetic pressure can we calculate mag field yet? And its pressure?

And as unfortunately I could not get an answer I answered myself:

Current of 444’000 Amperes with diameter 5mm produces about 17T mag field at its surface. This corresponds to ~1.15*10^8 Pa of mag pressure. This is about 3 times less than estimated by Mr. jamesr kinetic pressure. But Mr. jamesr probably assumes the temperature of combined beam has an order of center-of-mass collision energy (30keV). That will not be so. As nobody in the world could achieve the temperature in Z-pinch or TOKAMAK via only Ohmic heating more than fraction of 1keV (30 times less than 30keV) even running on much higher scattering cross sections and, so, much higher intensity of thermalization. And, so, [em]my estimation of achievable number density of 1E23-1E24m^-3 should be realistic[/em].

[Joseph Chikva]

jamesr wrote: I’ll leave you to figure out the magnetic field you need to contain that at a beta of less than 1.
Even if the pressure was highly anisotropic so the radial part was only a few percent of the total, the required toroidal field would be impossible to create on that scale.

Unlike TOKAMAK we need not the toroidal field stronger than poloidal at the surface of plasma (beam). Yes, in TOKAMAK the ratio of these two parameters has 50 order.
As:

For a current stream to retain its form as a beam, in which the longitudinal velocity exceeds the transverse velocity and also avoid ‘kink’ instability, it is necessary that v<<y.

COLLECTIVE AND COHERENT METHODS OF PARTICLE ACCELERATION, J. D. LAWSON, Rutherford Laboratory, Chilton, Berkshire, England
http://cdsweb.cern.ch/record/1107899/files/p21.pdf

And electron’s y in fixed frame of reference and ion-electron y is about 80.
The case when Budker’s parameter v=1 corresponds to linear density 3.6E14 m^-1 and electron current ~17’000A. And for demo reactor I am proposing only 4’000A (v=~0,25<<80)
Also Budker considers electron component in the Stabilized Relativistic Electron Beam as flexible rod with certain rigidness around and in potential well of which the ions’ beams move. And relatively weak longitudinal mag field only should improve the rigidity.
We will have poloidal field at the surface of combined beam ~17T and there also would be enough to create “weak” toroidal field ~4T without using superconducting magnets.
As similarity of mag fields configuration with TOKAMAK does not mean that all criterions (limits) written for TOKAMAK (Kruskal-Shafranov, Troyon, etc) would be applicable for proposed Concept as well.
• Plasma in TOKAMAK is quazineutral unlike the Concept.
• There are not in TOKAMAK high relativistic electrons unlike the Concept.
• Bremsstrahlung in TOKAMAK is not considered as one of stabilizing factors unlike the Concept.
• Temperature in Concept at least on order of magnitude lower than in TOKAMAK.
• Etc.

[Joseph Chikva]

Instabilities

In spite of the fact that mag field configuration of proposed Concept is very similar to TOKAMAK (combination of toroidal
and poloidal fields), stability limits written for TOKAMAK (Kruskal-Shafranov, Troyon, etc) are not quite applicable

As:
Plasma is quazineutral in TOKAMAK unlike the Concept
There are not high relativistic electrons in TOKAMAK unlike the Concept
Bremsstrahlung is not considered as one of stabilizing factors in TOKAMAK unlike the Concept
Temperature in a beam by the Concept is at least on order of magnitude lower than in TOKAMAK
Etc.

Kink Instability
Electron component is high relativistic and it is well known that in case when v<<γ beam does not suffer kink instability even
without usage of external stabilizing factors (such as axial mag field, conductive wall, etc.). And electron beam provides some
“rigidity” to the combined beam.
Here:
v = Ne^2/m0c^2 is so called Budker’s parameter in which N is the number of electrons per unit of length
( v = 1 corresponds to case when N = 3.6E14 m^-1 and electron current equal to 17’000 A)
On the contrary, ionic component has a high v with γ close to 1 (v > 1), produces strong poloidal mag field at the surface and
should be stabilized from externally. But the fact that ions move along the axis and in potential well of “rigid” electron beam together with the stabilizing factor of comparatively weak toroidal field allows to hope on immunity against on at least short wave kink instability.
Long wave kink instability can be eliminated by electrostatic quadrupoles (usage of such quadrupoles is proposed also for HIF)

Transverse Instabilities
Transverse Instabilities such as:
Betatron waves
Beam breakup instability
Transverse resistive wall instability
Hose instability
Etc.
may be damped effectively as something like “friction” is observed in combined beam.
Radiative “friction” by which via collective momentum interchanging all charged particles having transverse velocities moving in a
very strong poloidal mag field dissipate energy via Bremsstrahlung

Longitudinal Instabilities
Longitudinal Instabilities such as:
Two-stream instability
Negative mass instability
Longitudinal resistive wall instability
Etc.
can not be dumped effectively only by radiative “friction”.
But also it is well known high relativistic factor slows two-stream instability’s development rate and there are number of papers in
which is stated that comparatively weak longitudinal mag field dramatically expands stability area.
So, proposed concept will have immunity on at least electron-ion two-stream instability, electro-electron two-stream instability will
not be observed at all and ion-ion due to ions’ lower charge-to-mass ratio are less subject to this type of instability.
Also for ion-ion two stabilizing factors:
Longitudinal mag field
Certain initial spread of velocities
would be useful.

Negative mass instability should not be a problem for proposed Concept due to the fact that despite of non-neutral nature of combined beam, nevertheless ions are in negative potential well of electrons and electrons – in positive potential well. And there are not conditions
for grow of this type of instability in this case.

Regarding Longitudinal resistive wall instability: its growth or damping depends sensitively on the axial velocity distribution of particles near the phase velocity (when damps – Landau damping). And by Neil and Sessler the rule for stability here is that the spread in circulation frequency must be near the certain value.

[Author]

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