When Will Fusion Work? Insights from ITER and Expert Opinions

[PAllen]

Please forgive me, but I thought this was a forum where you can ask questions and thereby cut some corners with regard to how much "useless" information there is out there.

It's almost like when you are discussing things with a person who owns a smartphone. He immediatelly and happilly pulls it out when the answer to the question seems googleable.

But what happens? Well he googles up the information but while he is doing this he gives me lots of unrelative and uninteresting information and I bet that all of this never takes less than ten minutes.

So I am just trying to cut these corners, because I know there is lots of information about this stuff we are discussing here. But really, I have refused to confess this before because I think I know so little and is kind of embarassed about it, but I do hold a degree in Master of Science in Electronical Engineering even though I graduated 96. Which is 18 years ago, if you do the math.

I do however remember very little, as you have noticed, but I am really TIRED of reading books!

And I LOVE chatting with you guys!

So I simply want to refresh my "forgotten" knowledge and understand.

And I can not understand why it seems to be so hard for you to kindly help me.

Don't you like helping people, or what is wrong with you?

While I'm at it, I feel that scientifically skilled people like you are the modern worlds priesthood.

Another thing, D H "bragged" about knowing five decimals in g by heart. I know five decimals in pi by heart, but who cares!

Regards, Roger

Well, there are problems with your attitude that have shown up on this thread. Simultaneously claiming ignorance, yet rejecting explanations. Unwillingness to meet people half way in the thought and work department - a forum can never substitute for education (self education or formal). It is meant to help with specific question, not provide systematic education. When I was interested in fusion in elementary school, I wrote away to the USAEC for free pamphlets on controlled fusion that covered stellarators, pinch tubes, the reactions, the probabilities, and energy yields. Trying to get all of this question by question, spoon fed, is not reasonable.

 

[rogerk8]

Back to business...

Listing the statements I believe I understand:

5) The magnetic confinement in a tokamak is completely different from the gravitational "confinement" in the Sun.[mfb], 5

p=nkT in the Tokamak and g is "zero" so yes, there is a major difference.

I know that the cyclotron frequency for a proton is

$$w_c=\frac{|q|B}{m_p}≈10^8 [rad/Ts]$$

which indicates that the higher the B, the higher the v and thus higher temperature.

6) One definition of a planet versus and asteroid is a body large enough the gravity overwhelms all possible sources of mechanical rigidity, making the body round [PAllen], 5

I believe that my formula

$$p≈n_in_o\frac{(R-r)^3}{r}$$

is approximatelly correct.

So yes, gravitational pressure is increasing as we move inwards.

Note: The variables has been defined above.

10) The core of the sun has a density of about 150 grams/cm^3, well over 10 times the density of the Earth's core. This is because of the enormous pressure of the overlying layers squeezing an ionized plasma to a density beyond any material we know on earth. [PAllen], 5

Here I will take your word for the actual data. I will however try to find a relevant equation while I fully agree that the pressure is increasing inwards and the Sun is huge...

11) Even today, the core of the sun is neutral - the hydrogen is ionized and we have a plasma, but the negative electrons are still hanging around there together with the positive protons and helium nuclei. [mfb], 5

I recognize this reasoning and understand it as you have put it but I have my doubts about why it becomes ionized and why the first particles that began to build the Sun had to be neutral Hydrogen atoms.

I have shown above that

$$F_Q/F_G=10^{36}$$

which means that the gravitational force between two protons (or neutrons) is zero when compared to the electromagnetic force.

This however only means that the particles will have to be neutral to be able to bundle up.

So to me, it could equally have been neutrons (don't take this too seriously ).

[decays study emminent, my note]

20) The pressure at some point inside the Sun is equal to the weight of all the stuff above that point. [D H], 5

Roger that (finally )

21) Even though the Sun's core is a plasma (and hence a gas), it's is about eight times that of solid uranium at the Earth's surface [D H], 5 (even more amazing now )

Understood but equation needed.

22) It is the temperature and density that are ultimately responsible for fusion [D H], 5

Terrestial fusion would only depend on plasma pressure, i.e p=nkT.

High temperature and high density thus gives high plasma pressure.

Why fusion then suddenly starts is an enigma to me but we could now easily compare to the Sun with the enormous gravitational pressure where pressure obviously starts fusion.

23) The high temperature makes for particles with very high velocities [D H], 5

$$kT≈\frac{mv^2}{2}$$

24) The high density means *lots* of collisions between those fast moving particles. [D H], 5

Roger that (but not so obvious in my world, thanks!)

26) Roger, you are looking at P=nkT as saying that pressure is caused by the local density and temperature. Don't do that. Look at it the other way around, as saying that local density and temperature are determined by the pressure [D H], 5 (only true in stars though)

Rephrasing, not true in a Tokamak.

27) Moving radially into sphere, the area decreases. The pressure is determined by the area and weight of the atmosphere above. The weight is due to the mass being pulled to the center of gravity, by gravity. [Astronuc], 5

Already acknowledged. A formula would be greatly appreciated (but maybe I should search for it by my own )

Roger
PS
I hold a Master's degree in Electrical Engineering, not in Physics

 

[the_wolfman]

5) The magnetic confinement in a tokamak is completely different from the gravitational "confinement" in the Sun.[mfb], 5

p=nkT in the Tokamak and g is "zero" so yes, there is a major difference.

I know that the cyclotron frequency for a proton is
wc=|q|Bmp≈108[rad/Ts]


which indicates that the higher the B, the higher the v and thus higher temperature.

Nope. Recall the velocity is $v = \omega r$ where r is the the gyroradius. The gyroradius is the function of the velocity of a particle such that the above relation holds. The distribution of the of the velocities is a function of the temperature of the plasma. The gyrofrequency is independent of the velocity of a particle. (Technically its only the velocity perpendicular to the magnetic field. The parallel velocity is unconstrained by the magnetic field. )

I recognize this reasoning and understand it as you have put it but I have my doubts about why it becomes ionized and why the first particles that began to build the Sun had to be neutral Hydrogen atoms.

The degree to which a plasma/gas is ionized has nothing to due with the ratio of gravity and electrostatic forces. Its related to the a balance between the ionization due to neutral particle collisions and charge recombination between "free" ions and electrons. There is a famous equation called the Saha equation that describes this balance.

 

[rogerk8]

Nope. Recall the velocity is $v = \omega r$ where r is the the gyroradius. The gyroradius is the function of the velocity of a particle such that the above relation holds. The distribution of the of the velocities is a function of the temperature of the plasma. The gyrofrequency is independent of the velocity of a particle. (Technically its only the velocity perpendicular to the magnetic field. The parallel velocity is unconstrained by the magnetic field. )



The degree to which a plasma/gas is ionized has nothing to due with the ratio of gravity and electrostatic forces. Its related to the a balance between the ionization due to neutral particle collisions and charge recombination between "free" ions and electrons. There is a famous equation called the Saha equation that describes this balance.

Thank you for correcting me. This is what I want.

Obviously I haven't even understood my own blog.

Repeating for fun:

$$w_c=\frac{|q|B}{m_p}[rad/s]$$

which is called the cyclotron frequency.

$$r_L=\frac{m_pv}{|q|B}[m]$$

which is called the Langmor radius.

Looking at the formulas for the cyclotron frequency and the Langmor radius while multiplying them to yield the actual perpendicular frequency, just gave v as result.

This fact, along with me believing strongly (and stupidly) that the increase of B was one way of increasing v (and thus the temperature of the plasma), made me kind of conveniently ommit the Langmor radius thinking "while the cyclotron frequency obviously is proportional to B, v must be proportional to B".

Due to your thankful help, I now fully understand that B only confines the plasma.

A related question is thus how to actually heat up a plasma. One way I read about at ITER homepage was neutron-cannons. My layman understanding of this is that the actual collisions heats up the plasma.

But how to reach 150 million degrees is an enigma to me.

Finally,

Repeating my own description of the Saha equation for convenience:

-----
$$\frac{n_i}{n_n}=2.4*10^{21}\frac{T^{3/2}}{n_i}\exp-(\frac{U_i}{kT})$$

Where n_i is the ion density and n_n is the neutral atoms density and U_i is the ionization energy of the gas.

Putting for ordinary air

$$n_n=3*10^{25}m^{-3}$$
$$T=300K$$
$$U_i=14,5eV (nitrogen)$$

gives

$$\frac{n_i}{n_n}=10^{-122}$$

which is rediculously low.

And the ionization remains low until U_i is only a few times kT.

So there exists no plasmas naturally here on earth, only in astromnomical bodies with temperatures of millions of degrees.
-----

Analyzing this equation it is now finally clear that kT needs to approach U_i for any ionization to occur whatsoever.

This gets back to the problem of temperature increasement.

Or perhaps even what temperature really is.

To me, temperature is perpendicular velocity. But there has to be parallell velocity too, right? And in solids I would even dare to say that temperature is vibrations.

But what about collisions? Do perhaps the actual collisions themselves give rise to temperature in some mysterious way other than increasing the speed of the particle it is colliding with?

This last part is only me, with my obviously limited physics knowledge, speculating. Don't take it too seriously.

Roger
PS
I kind of doubt that the Saha equation is that famous

 

[the_wolfman]

There are 5 ways we commonly heat a plasma relevant to fusion :
1) Ohmic heating. You run a current through a plasma and this creates heat due to electrical resistance.
2) Wave heating. We use antennas to inject electromagnetic waves into a plasma. The plasma absorbs these waves and converts their energy into heat. Similar to a how a microwave heats leftovers.
3) Neutral beam heating. We inject beams of high energy neutral particles into the plasma. As the particles collide with the plasma they slow down and their kinetic energy is converted into heat.
4) Compressive heating. When you compress a plasma you do pdv work on it just like any other fluid. This work in turn heats the plasma.
5) Alpha particle heating. If you get fusion to occur, high energy alpha particles are produced. They then heat the plasma as they slow down.

There are actually two ways to "produce" a plasma. One is to go to high temperature, but you can also go to ultra low density. This can be qualitatively in the Saha equation due to the quadratic dependency of the ion density (however in many low temperature plasmas the Saha equation is not strictly valid). There are plasmas that occur naturally on earth. Lightning is one example. The auroras are another.

Temperature has little to due perpendicular velocity. Temperature is the random kinetic energy of a collection of particles. There is also a directed kinetic energy that gives rise to mean flow. (There are more precise definitions but this is sufficient for plasma physics). In magnetic confinement, we sometimes define temperatures parallel and perpendicular to the magnetic field, but that is a pretty advanced topic.

Fame is a relative term. In physics when an equation has a name, its a famous equation.

 

[rogerk8]

There are 5 ways we commonly heat a plasma relevant to fusion :
1) Ohmic heating. You run a current through a plasma and this creates heat due to electrical resistance.
2) Wave heating. We use antennas to inject electromagnetic waves into a plasma. The plasma absorbs these waves and converts their energy into heat. Similar to a how a microwave heats leftovers.
3) Neutral beam heating. We inject beams of high energy neutral particles into the plasma. As the particles collide with the plasma they slow down and their kinetic energy is converted into heat.
4) Compressive heating. When you compress a plasma you do pdv work on it just like any other fluid. This work in turn heats the plasma.
5) Alpha particle heating. If you get fusion to occur, high energy alpha particles are produced. They then heat the plasma as they slow down.

I wish to study these methodes of heating. Unless you feel like explaining? Just kidding, some kind of work I really have to do by my own. But it would be nice if you could direct me to some links.

In the meantime I wish to use my slowly growing knowledge in applying my own thoughts:

1) Being an Electrical Engineer, I kind of understand this. However, how a current actually is run through the plasma is hard to understand. But maybe transformer theory applies. This would mean that the actual "ring" of plasma may be considered "one turn". All you need now is a coupling factor which may be made by placing a coil directly above the Tokamak.

I really wonder how far off from the truth I am with this. But it sounds reasonable to me.

2) Knowing a bit how a microwave owen works, i.e injecting 2.45GHz into our water-based food which makes the water molecule resonate, I kind of understand this methode.

3) This sounds like my "neutron-cannon" above and is relatively easy to understand as you have explained it.

4) This gets back to my recent thoughts about my statement that a magnetic field only confines a plasma. Because turning up B would actually mean a smaller Langmor radius and thus a higher density, right?

For a while I thought that p=nkT could be used. But all I can see is that pressure is increased (while T remains constant).

On the other hand, there should be much more collisions now. And as I've learned, collisions makes for higher v and thus T, right?

So the conclusion must be that higher B actually heats the plasma (at least to some extent).

5) So these Helium nucleus are the once that will make the fusion reaction "persist"?

There are actually two ways to "produce" a plasma. One is to go to high temperature, but you can also go to ultra low density. This can be qualitatively in the Saha equation due to the quadratic dependency of the ion density (however in many low temperature plasmas the Saha equation is not strictly valid). There are plasmas that occur naturally on earth. Lightning is one example. The auroras are another.

Rewriting the Saha equation just for fun:

$$n_i^2≈n_n T^{3/2}\exp-(\frac{U_i}{kT})$$

Even when I rewrite it I fail to understand, though.

If the ion density is low the neutral atoms density would have to be high, unless T is high (?)

I also fail in understanding how the Saha equation may be applied in a Tokamak. This is because I believe that what you do when you start your experiement is that first you start the B, then you inject the protons (for simplicity). And you can only inject charged particles because neutral particles would only "fall to the floor" i.e are not confined by B.

Temperature has little to due perpendicular velocity.

This a surprise to me.

Temperature is the random kinetic energy of a collection of particles.

Very educational.

There is also a directed kinetic energy that gives rise to mean flow.

This I kind of understand. But only in the sense that heat flows from "hot to cold" (?)

In magnetic confinement, we sometimes define temperatures parallel and perpendicular to the magnetic field, but that is a pretty advanced topic.

Actually, when you tell me this I think I have read something about it in my plasma physics book. I do however think that it is too early for me to even try to understand this.

Finally I wish to thank you for your nice reply. This is getting more and more interesting by the hour!

Roger

 

[rogerk8]

I kind of understand how ohmic heating might work. However, how a current actually is run through the plasma is hard to understand. But maybe transformer theory applies. This would mean that the actual "ring" of plasma may be considered "one turn". All you need now is a coupling factor which may be made by placing a coil directly above the Tokamak.

This is a crazy and stupid idea.

Ohmic heating would mean running current through the plasma with f.i the use of two electrodes placed at the diameter.

A coil placed like the above would however create a poloidal magnetic field which is used to further confine the plasma.

Compressive heating gets back to my recent thoughts about my statement that a magnetic field only confines a plasma. Because turning up B would actually mean a smaller Langmor radius and thus a higher density, right?

For a while I thought that p=nkT could be used. But all I can see is that pressure is increased (while T remains constant).

On the other hand, there should be much more collisions now. And as I've learned, collisions makes for higher v and thus T, right?

So the conclusion must be that higher B actually heats the plasma (at least to some extent).

Further reflections tells me that pumping B in such a way that B is slowly incresed, fastly decresed and slowly increased again should give higher and higher T.

This is because the velocity of particles would not have the time to adapt to the lower B (i.e higher Langmor radius and therefore lower density) before the higher B is once again applied.

Can there be any truth whatsoever in this?

On the other hand, Wolfman has told me that temperature has little to do with perpendicular velocity.

Roger
PS
For a while there I actually considered building a Tokamak on my own

But the below reasoning made me forget that thought.

Here is only a short and preliminary version of my exciting project that not only is intended for fun but for educational purposes also:

I will use ohmic and "magnetic" heating on a bunch of electrons.

I will use a circular hollow glass tube.

With regard to the Aurora-effect it might even be useful to use a nonevacuated tube. The different colors of air (i.e Nitrogen and Oxygen ionization mainly, right?) would then tell me the temperature of the plasma while I'm heating it up.

The electrons will be injected by putting a filament inside the tube and then just close it with some rubber plug.

AC-heating this filament with a transformer makes it potentially float. I will mount a high ohmic resistor to ground though to really repell the electrons once the filament has been turned off.

Heating the filament would then produce electrons as a cloud outside the filament/cathode.

The heating is then turned off and some electrons will be available inside the tube.

All around the circular tube I will place C-core transformers.

These transformers will generate the toroidal B.

Directly opposit the filament I will place an electrode/anode.

Applying a voltage at anode would then give a current like in a vacuum tube.

The current in a vacuum diode is defined by:

$$Ia≈\frac{A}{d^2}V^{3/2}$$

A huge d would thus give a very small Ia.

But we are not interested in high Ia (other than ohmic heating).

We are interested in increasing the temperature of the electrons.

Considering this, I now understand that ohmic heating is out of the question in this case because the electrons would just disappear from the tube (while protons can not and thus are suceptible to electron ohmic heating).

RF-heating could be used but I did a (Newtonian) calculation of the cyclotron frequency for an electron in a 1T magnetic field. It was some $10^{11}$ rad/s which must be wrong or unappliciable. But I think I read something about this at ITER homepage and especially that the RF for DT-fuel would be some 100GHz or something.

Anyway, I think that the RF frequency for heating up the electrons this way is way beyond what I can build. The highest oscillating frequency I have ever built was a Hartley oscillator of some 25MHz

So finally, the only methode I have left to heat up my plasma of electrons is magnetic pumping (=compressive heating?). This however is a methode I have thought up by myself and considering your nicely provided fact that perpendicular velocity has little to do with temperature, it kind of makes me give up my crazy project even before I have started it

But really, it was fun and educational to think it up and learn along the way.

 

[rogerk8]

Listing the statements I kind of understand:

1) The higher temperatures (for DT fuel, my note) are needed to counter the lower pressure in the reactor, with a higher required power density [mfb], 3 (power density, not understood)

Relevant pressure is plasma pressure (p=nkT) and not gravitational pressure so this part I understand.

Plasma pressure has the unit J/m³ and thus N/m² so yes, it may be called pressure.

J/m³ may also be written Ws/m³ which may be interprated as power times time devided by m³.

Looking at a single second this leads to W/m³ which may be interprated as "power density".

But it tells me nothing

2) Because the power output of a single cubic meter of solar core material (i.e. ordinary hydrogen, proton-proton fusion) is roughly on par with a toaster oven [mheslep], 1 (is it really that bad?)

With regard to the huge size of the Sun I kind of understand this.

3) Pressure is limited by the magnetic fields (in a Tokamak, my note)- a higher temperature does not allow to increase pressure, so the volume density will go down. As the interaction probability rises quickly with temperature, this still leads to a higher fusion rate [mfb], 1 (why not higher pressure? And fusion rate, how is that defined?)

Why?

4) The sun, including the core, is electrically neutral. Both ions and electrons exist under very height pressures at the core.[Drakkith], 4 (electrically neutral sounds convenient, though)

Roger that.

7) Also remember that the Sun has electrons and is not charged overall. The atoms in the gas cloud that initially collapsed to form the Sun didn't repel each other because they were not ionized.[Drakkith], 4 (the post Big Bang soup should have been be more elementary, I believe)

Roger that.

8) By the time you need to worry about proton repulsion (in the Sun, my note), you already have the 250 billion kg/cm^2 pressure of neutral matter above to overcome it.[PAllen], 3 (why suddenly not neutral? What happens under high pressure?)

This sounds reasonable.

9) Correct in that the starting point (for the Sun, my note) is Hydrogen gas. However, the fusion reaction is not to Helium 2, which would not release energy. It is to Deuterium when the proton-proton interaction is accompanied by emission of a positron and a neutrino. This process releases energy but is very rare.[PAllen], 1 (but very interesting).

So p + p somehow yields "p + n" (+ positron + neutrino)?

Recalling what you so kindly have said before, a neutron may decay to a proton but a proton, being slightly lighter, may not unless accompanied by some energy, right?

So first we have p + energy -> neutron + neutrino + positron

Then we have p + p -> D + positron + neutrino.

As I've said before, this is very interesting and I must study this further.

12) as it (the neutral Hydrogen, my note) collpased and heated (you can think of this simply as conversion of gravitational potential energy to heat), the center became ionized, but still neutral on average. You than have a neutral plasma at high temperature and pressure (= high density), such that the rare p + p -> deuterium + neutrino + positron can occur (at a low rate per volume). [PAllen], 2 (why ionized?)

Already acknowledged.

13) p + p -> deuterium + neutrino + positron [PAllen], 0 (but extremely interesting)

Already acknowledged.

14) The g (in a .1 lightyears wide cube of Hydrogen, my note) is varying during the collapse, but it should be easy to imagine that you have an enormous amount of energy per unit compressed volume of hydrogen. [PAllen], 2 (no, it's not easy)

If energy is kT and could be related to gravitational pressure (and thus density increasement) pressure is indeed high.

Looking at pressure as J/m³ I now finally understand what you mean!

Pressure is simply "Energy per Volume"!

But it is still an enigma how T is changed.

15) Normally, a neutron decays via weak interaction (in about 10 minutes if outside of a nucleus) into proton, an electron, and an anti-neutrino [PAllen], 0 (but extremely interesting)

This I would very much like to understand!

Repeating for convenience: p + energy->neutron + positron + neutrino

16) Since a proton is slightly lighter than a neutron, it does not decay (by any standard model processes). However, a proton plus energy, can, with low probability, undergo the 'decay' p -> neutron + neutrino + positron, mediated by the same weak interaction [PAllen], 0 (but extremely interesting)

Already acknowledged.

17) In the core of the sun, where the high temperature give each proton plenty of KE, and the high density makes collisions likely, once in a blue moon this reaction occurs along with with a collision. When it does, the formation of deuterium releases net energy (not much, but enough to keep things going). [PAllen], 1

So p + p not only gives D + neutrino + positron

it also gives energy?

18) You are ignoring pressure, density, and temperature, and you are also ignoring the fact that the Sun is electrically neutral. [D H], 4 (electrically neutral sounds as convenient as the useful law of conservation of energy)

I now understand this.

19) While the gravitational force between two protons is exceedingly small, the mutual gravitational interaction amongst the ~10^57 protons and neutrons in the Sun is extremely large. This is what is responsible for the extremely high pressure at the center of the Sun [D H], 1 (what mutual gravitational interaction? And how can this give a high pressure?)

High density gives high pressure.

25) You need to think when you see a very large number such as 250 billion atmospheres. Think about what it means in terms of pressure and temperature [D H], 3 (still just a huge number )

Roger that.

28) Terrestrial fusion plasmas use d+t fusion, because it is easier, but has the disadvantage that most of the energy is released to the 14.1 MeV neutron, which means it has to slow down and be captured in some blanket, which is heated and the heat is then passed to a working fluid, which is then used in some thermodynamic [Astronuc], 3 (please explain "easier")

Still interested in why.

Roger
PS
The thoughts of building a Tokamak of my own has been renewed.

Today my colleague (holding a Master's degree in Physics while being a technical oracle) explained to me how a luminance tube (LT) works.

He told me that the LT has a lightly pressurized Mercury vapor inside. And wrote the actual electrical configuration of it all down on an paper sheet in about two minutes.

It obviously consists of two heaters/filaments at either end, an inductor in series with the AC and a glimm lighter that is shorted at power up but releases after a short while which makes the inductor spike the voltage so high that the Mercury vapor ignites. This in turn makes the luminant coating of the inside of the tube shine, which is what we see.

Obviously still not understanding Saha and thus what a plasma really is, I would insist on calling this a plasma.

This is because we here have both "free" electrons and Mercury ions, right?

In my stupid electron "plasma" we did however not have any ions, only Nitrogen and Oxygen atoms.

So I am rethinking like this:

Let's build a proton cannon (or perhaps more generally, an ion cannon).

Let's build it like a CRT, accelerating the ions with a high voltage.

The velocity of the ions may then be determined by:

$$\frac{mv^2}{2}=qU$$

Considerations:

1) I wish to chose the gas
2) Hydrogen is dangerous
3) A pressurized cannister of Hydrogen might be heated by a Bunsen burner for even more ions
4) The system needs to have several valves
5) Gas diffusable membranes might be used to confine the gas/ions to be accelerated.
6) Evacuating the tube would give a negative pressure, sucking the gas thru the membrane.
7) Turning on the toroidal B.
8) Opening the main valve and turning on the ion cannon.
9) Turning on Ohmic heating (i.e running electrons thru the ions/plasma)
10) Adjusting B and watching the plasma glow more and more (or even change color)

The main interest with this is to be able to see the color of the plasma change somewhat with regard to me changing B and the Ohmic heating and thus the temperature of the plasma.

This is my number one joy with this project.

Now, what gas should I use?

I have obviously thougt of Hydrogen but it sounds dangerous to say the least and it really is not that important to mimmic a fusion reactor that closely.

So I'm thinking of other gases. Pure Nitrogen, perhaps.

I don't think Nitrogen ions are that dangerous. And Nitrogen obviously gives nice colors (Aurora).

So perhaps I should try to get me some pressurized Nitrogen in a cannister. Should not be that difficult because both racing cars and hospitals use it(?)

Ionizing the Nitrogen could perhaps be done by heating it up with a Bunsen burner.

The question is how much I have to heat it up to be able to inject ions into my tube Tokamak.

Considering the Saha equation, it strikes me that the high pressure (and thus density) itself makes ions being available without heating it up.

But this depends on how much it is actually pressurized.

But really, going from $10^{-122}$ to some $10^{-10}$ is a huge step. To say the least

 

[rogerk8]

Listing your nicely provided links:

1) http://upload.wikimedia.org/wikipedia/commons/d/d0/Fusion_rxnrate.svg [mfb]

Depending on what "reaction rate" really is this graph clearly tells that DT-fuel requires the lowest temperature to ignite(?) when compared to DD-fuel and DHe₃-fuel.

2) http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html [Astronuc]
3) http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c1 [Astronuc]
4) http://www.umich.edu/~gs265/star.htm [Astronuc]
5) http://hyperphysics.phy-astr.gsu.edu/hbase/astro/procyc.html [Astronuc]
6) http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html [Astronuc]
7) http://csep10.phys.utk.edu/astr162/lect/energy/cno.html [Astronuc]
8) http://hyperphysics.phy-astr.gsu.edu/hbase/pertab/h.html [Astronuc]

I will study these links now collected and get back to you with the most interesting parts.

But for now I wish to get back to my Tokamak project.

Considering the function of the luminance tube (LT).

Considering the fact that the density of the gas may be "ultra low" for a plasma to occur.

My toroidal circular tube may then be filled with ordinary air at 1 atm of pressure.

The air may then be ignited by the same procedure as the LT.

This would give me a pinkish glow as in a leaking vacuum tube, right?

Adjustments of B would then give me a radial change of the plasma while at the same time making it shine brighter at higher B, right?

So the most fun part would thus be to be able to adjust B and watch the plasma change.

Ohmic heating of the plasma would be possible by simply increasing the voltage (i.e current).

This would also affect the brightness of the plasma.

All of this may be possible due to the actual function of a LT i.e:

1) Turning on the LT gives high currents thru the filaments (I will use two at the diameter).
2) After a short while the glimm lighter releases and the inductor spikes a high voltage.
3) This voltage "ignites" the air making it a plasma of electrons and Nitrogen ions (mainly)
4) Current continues to flow and thus makes the filaments continue to be warm

1) This is not that strange.
2) This is also not so strange (while the actual function of the glimm lighter is not understood).
3) I really do not understand this. Why would a high voltage (like lightning) "ignite" the air? And what will the color be? Lightning is white, Aurora is green and red...And why will it "ignite" in the first place? Lightning may be interpreted as an extremelly high voltage which overcomes the dielectric strength of air and thus "strikes" but what about my case? Is it the same here, somehow?
4) This has been explained to me to be true in a LT. But would it be true in my case. If so, why?

Roger
PS
It seems like my Tokamak project more and more just assembles a luminance tube

 

[rogerk8]

2) http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html

Clicking around in this interesting link gave these interesting facts:

$$\frac{mv^2}{2}≈kT[J]$$

$$PV=nRT=NkT[Nm]$$

n=number of mols, N=number of particles

$$W=PdV[J]$$

which means that the work done by the gas is the pressure times the volume increasement.

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c3

I like the above graphical explanation of the Maxwellian velocity distribution which has to do with the Boltzmann distribution function:

$$f(v)=A\exp-{E_k/kT}$$

where

$$v_p=\sqrt{\frac{2kT}{m}}\approx\sqrt{\frac{T}{m}}[m/s]$$

is the most probable speed.

This does however not mean that I understand it

I think this will suffice for today. I will get back to this later on. There is lots to read

Roger
PS
I think the Saha equation is somewhat wrong or at least misguiding. There do excist plasmas in nature:

1) The Lightning
2) The Aurora
3) Corona discharge (man-made though, I still wonder what makes the beautiful blue light)
4) Glows of different colors in functional/malfunctional vacuum tubes (also man-made though)
5) Luminance tubes (also man-made)

I have read some about Corona discharges and it's fascinating!

 

[rogerk8]

2) http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html
3) http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c1

I have now read almost all information in the so nicely above provided links.

Specific heat: The energy resistance for temperature/KE increasement.

Entropy:
1) Describes the disorder of a system
2) In time an isolated system will have higher entropy (i.e be more chaotic)

Thermodynamics: Heat and work is interchangeable and only means that the internal energy has been increased.

First law of thermodynamics:
$$dU=Q-W$$
where dU is the change in internal energy, Q the heat added to the system and W the work done by the system.

Finally, an amazing integral just for fun:
$$\int_{-\infty}^\infty e^{-x^2}dx=\sqrt{\pi}$$
Because it is not enough that pi is an extremely fascinating number which seems to have no end, this integral actually gives the answer as the square root of pi!

Roger
PS
Astronuc, I totally LOVE your links! Especially no 5 i.e:
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/procyc.html
which I'm hooked at right now.

 

[rogerk8]

2) http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html
3) http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c1
5) http://hyperphysics.phy-astr.gsu.edu/hbase/astro/procyc.html

Standard model:
1) electron and positron ("anti-electron")
2) muon and anti-muon
3) tau and anti-tau

Along with these comes their neutrino and anti-neutrino which gives six distinct types of particles or:

1) electron
2) electron-neutrino
3) muon
4) muon-neutrino
5) tau
6) tau-neutrino

The neutrinos being preliminary mass-less.

The dominant three of these are fundamentals and consist of quarks. For our purposes it is enough to recognize two types of quarks namely the up-quark and the down-quark. This is due to the fact that a neutron consists of two down-quarks and one up-quark while a proton consists of two up-quarks and one down-quark.

And as you people so kindly have explained above a neutron can undergo weak interaction and be converted to a proton and a anti-neutrino. This has to do with the fact that a quark can change it's type/flavor. In this case one down-quark "only" has to change to one up-quark to make the change of the particle.

It has also been explained above how a proton can be changed to a neutron (transmutation) in a similar manner.

This is the basic reason for all those protons (read Hydrogen atoms) at the bearth of a star like our Sun can generate neutrons and thus Deuterium to actually start the fusion process to Helium.

The above link does unfortunatelly not tell so much "useful" about the Muon or the Tau. It does however say that Muons make up more than half of the cosmic radiation at sea level and that it is quite massive relative to the electron. This while the Tau is much more heavier.

Proton-Proton Fusion:

1) Protons fuse
2) One proton is transmuted into one neutron forming Deuterium (releasing one positron and an electron-neutrino).
3) Deuterium fuses with another proton (which also seems to release gamma-rays)
4) Two of the resulting Helium_3 neclei fuse
5) An Alpha particle (Helium_4) forms with the energetic release of two protons to complete the process.

A fun quote by Arthur Eddington:

"I am aware that many critics consider the stars are not hot enough. The critics lay themselves open to an obvious retort; we tell them to go and find a hotter place."

Getting back to thermodynamics.

The internal energy is obviously defined as the sum of KE and PE where KE is the kinetic energy (and by definition, the temperature) while PE or the potential energy (my guess) is what?

Specific heat seems to tell that the greater the sum of KE and PE is, the more energy is needed to heat it up.

For a while there I thought you may view the internal energy as constant like you may do in other closed systems like the gravitational sling shot for instance. But then I realized that energy (heat, in this case) is actually applied from outside the system. So PE (whatever that is when it comes to gases) would not lessen as we apply more KE. Because if it would, there would be a limit on how hot we can make a gas.

Specific heat may also be viewed as proportional to the internal energy. Large internal energy may be compared to a large equivalent mass (GR?) and would mean more energy applieance to get the same temperature.

May there be any truth in this?

Roger
PS
Astronomy is just theories.