When will fusion energy become commercially viable?

[mfb]

Pressure is limited by the magnetic fields - 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 (up to roughly 1 billion K for DT).

 

[rogerk8]

Interesting graph!

Let's kind of begin from the beginning. Consider the sun. Protons have somehow bundled up out of nowhere. These ions bundle up more and more until gravity(?) makes them bundle up so tight (in spite of their equal and repelling charge) that fusion to Helium starts and an enormous amount of energy is released. In the same time volume density and thus pressure is kept tight due to gravity and protons being abundant.

How far from the truth am I?

How important is the magnetic fields created by the moving ions (currents) for confining the fusion reactions to the core of the sun?

To me it feels like these currents might not necessarily contribute in a collective manner. The generated magnetic fields might as well be stocastic in direction and thus not be a true inspiration for a Tokamak.

Roger

 

[Drakkith]

The sun, including the core, is electrically neutral. Both ions and electrons exist under very height pressures at the core.

I don't know for certain but I don't believe that magnetic fields play much, if any, role in fusion in the Sun's core.

 

[mfb]

Magnetic fields are not relevant for fusion in the sun.
Pressure due to gravity is dominant. As a really simplified model, you can use Earth as comparison - the lower you are, the higher the pressure.

The magnetic confinement in a tokamak is completely different from the gravitational "confinement" in the sun.

 

[rogerk8]

Thank you for your educational information!

But I'm a stupid guy. When it comes to the birth of a star like our sun I do not understand how gravity can play such an important role.

Protons are positively charged, right?

And equal charge repell, right?

Still protons have obviously bundled up.

Why or more scientifically, how?

It is not enough that protons bundle up, they bundle up so tightly that they start to fuse into Helium.

I don't get this part.

Roger

 

[PAllen]

Thank you for your educational information!

But I'm a stupid guy. When it comes to the birth of a star like our sun I do not understand how gravity can play such an important role.

Protons are positively charged, right?

And equal charge repell, right?

Still protons have obviously bundled up.

Why or more scientifically, how?

It is not enough that protons bundle up, they bundle up so tightly that they start to fuse into Helium.

I don't get this part.

Roger

The pressure at the center of the sun is about 250 billion kg / cm ^2, and this is all due to gravity. Does this help?

Also, why are planets round? 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. A moon mass collection of diamond crystals will 'collapse' into round mass carbon, overcoming the rigid resistance of diamond. Now, how many times more massive is the sun than the moon?

 

[Drakkith]

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.

 

[rogerk8]

I know so little and understands so little so maybe I should quit now?

Anyway here is how I see it:

$$F_G=G\frac{m_1m_2}{r^2}[N]$$

$$F_Q=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}[N]$$

where for protons

$$m_p=1,67e^{-27}[kg]$$
$$G=6,67e^{-11}[Nm^2/kg^2]$$
$$q=+e=1,6e^{-19}[As]$$
$$\epsilon_0=8,85e^{-12}[As/Vm]$$

which gives

$$\frac{F_Q}{F_G}=10^{36}$$

This clearly states that, in the beginning, protons could not have bundled up due to gravity while the electromagnetic force is way much higher (to say the least).

So what happened? I see two scenarious:

1) The first particles to bundle up was neutrons and when they bundled up tight enough they somehow mutated into protons which after a while where able to fuse into He_2.

2) Reading your kind answer makes me think that perhaps the first neutral (which is a must here) particles where neutral protons i.e pure H_1 which later fuses into He_2.

Now I will try to answer your question "How many times more massive is the sun than the moon": I have no clue To me the sun is of course massive but it is also gasous like a plasma, right? So, stupid as I am, I would actually consider the moon to be more massive than the sun because it is made of dirt, so to speak. Please, educate me some more here if I'm wrong.

Roger
PS
I kind of know how to write isotopes but I fail using <sup>.

 

[PAllen]

I know so little and understands so little so maybe I should quit now?

Anyway here is how I see it:

$$F_G=G\frac{m_1m_2}{r^2}[N]$$

$$F_Q=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}[N]$$

where for protons

$$m_p=1,67e^{-27}[kg]$$
$$G=6,67e^{-11}[Nm^2/kg^2]$$
$$q=+e=1,6e^{-19}[As]$$
$$\epsilon_0=8,85e^{-12}[As/Vm]$$

which gives

$$\frac{F_Q}{F_G}=10^{36}$$

This clearly states that, in the beginning, protons could not have bundled up due to gravity while the electromagnetic force is way much higher (to say the least).

So far, so good, in the Newtonian sense. However, as Drakkith noted, the sun is electrically neutral, and started from Hydrogen atoms (and other stuff). By the time you need to worry about proton repulsion, you already have the 250 billion kg/cm^2 pressure of neutral matter above to overcome it.

Now, for the more remarkable GR correction to the Newtonian picture (though this is not relevant to the formation of stars). Suppose you put one proton in a cubic meter of vacuum, building this pattern out. According to GR, there would come a point, as you built this outwards, where this framework was within its Schwarzschild radius, despite the ultra-low density. Then, no matter what, the assemblage would collapse to a singularity, no matter what forces applied to the protons. The progress toward the singularity would be exactly mathematically and physically equivalent to the progress of time, so even forces approaching infinite would not be able to stop the collapse. Thus, per GR, enough stuff, however sparse, must collapse - if you have enough of it.

So what happened? I see two scenarious:

1) The first particles to bundle up was neutrons and when they bundled up tight enough they somehow mutated into protons which after a while where able to fuse into He_2.

No, much simpler, it started as Hydrogen atoms.

2) Reading your kind answer makes me think that perhaps the first neutral (which is a must here) particles where neutral protons i.e pure H_1 which later fuses into He_2.

Correct in that the starting point 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. The further steps from here to Helium 4 occur and much higher rates and release much more energy.

Now I will try to answer your question "How many times more massive is the sun than the moon": I have no clue To me the sun is of course massive but it is also gasous like a plasma, right? So, stupid as I am, I would actually consider the moon to be more massive than the sun because it is made of dirt, so to speak. Please, educate me some more here if I'm wrong.

Roger
PS
I kind of know how to write isotopes but I fail using <sup>.

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.

 

[phyzguy]

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.

There is also the fact that the volume of the sun is over 60 million times larger than the moon.

 

[mfb]

And the fact that Earth plus moon orbit the sun, not the other way round.

WolframAlpha: (mass of sun)/(mass of moon)

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.

 

[rogerk8]

Another fun calculation is:

$$F_G=F_Q$$

or

$$GMm_p=\frac{e^2}{4\pi\epsilon_0}$$

which gives

$$M=2 [Gkg]$$

which of couse is the same as the mass for

$$N_{mp}=10^{36}$$

number of protons.

However, this states that the mass of the rising sun has to exceed 2GKg before any protons may be attracted.

This still makes me believe that the sun began as a bundling up of neutrons which later on gave rise to such a high mass (>2Gkg) and therefore gravitational force that it could attract protons. Now when it did that, the rising sun got charged and due to the sign of charge of electrons they came along too.

As you may have noticed I am considering the simplest form of particle soup here which means that we already have a post Big Bang soup of convenient elementary particles. All of them in a plasma state.

So in the core we now have a plasma of both neutrons, protons and electrons.

But why did protons start to fuse?

I don't understand the concept of pressure for instance.

Repeating the formula here for convenience:

$$p=nkT[J/m^3=N/m^2]$$

Loooking at this formula you can see how increased particle density give rise to an increased pressure.

But what about T?

What determines T?

I don't get it.

Finally, gravitational force is of course higher the closer you get to the centre of gravity.

But what makes the pressure and/or gravitational force start the reaction to fuse?

What happens here with the elementary soup of star-life?

Roger

 

[PAllen]

Are you even reading other people's posts? I think about 5 times it has been explained the sun began with neutral hydrogen gas. The, as it 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).

 

[rogerk8]

I am of course reading other people's posts. But when people come with explanations like the GR I am totally lost and it's no use to even debate. Furthermore, I am trying to understand this my own way if this is alright by you?

Ok, let's say the sun began as a neutral Hydrogen gas. I can easily buy that.

Please explain how gravitational potential energy can be converted to heat. I don't even know what gravitational potential energy is (other than mgh).

And please explain p+p->deuterium (H_2) + neutrino + positron because I find this very interesting mainly due to the fantastic mutation of a proton becoming a neutron (i.e deuterium).

Finally, I thank you for your answer.

Roger

 

[PAllen]

I am of course reading other people's posts. But when people come with explanations like the GR I am totally lost and it's no use to even debate. Furthermore, I am trying to understand this my own way if this is alright by you?

Ok, let's say the sun began as a neutral Hydrogen gas. I can easily buy that.

Please explain how gravitational potential energy can be converted to heat. I don't even know what gravitational potential energy is (other than mgh).

mgh is good enough for the basic idea. You have a large mass of hydrogen in a cube .1 light years on a side. Under the influence of self gravitation, it collapses to a diameter of 1 million miles (appx). That means the average h in mgh, for given volume of hydrogen is about 100 billion miles. The g 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.

And please explain p+p->deuterium (H_2) + neutrino + positron because I find this very interesting mainly due to the fantastic mutation of a proton becoming a neutron (i.e deuterium).

Normally, a neutron decays via weak interaction (in about 10 minutes if outside of a nucleus) into proton, an electron, and an anti-neutrino. 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. 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).

Finally, I thank you for your answer.

Roger

 

[rogerk8]

I sincerelly want to thank you for putting so much time and effort into trying to explain these things to me. I feel honored!

I did not understand much though

So I will have to think about this before I can get back to you with adequate questions.

Take care!

Roger

 

[mfb]

This still makes me believe that the sun began as a bundling up of neutrons which later on gave rise to such a high mass (>2Gkg) and therefore gravitational force that it could attract protons. Now when it did that, the rising sun got charged and due to the sign of charge of electrons they came along too.

"I don't understand the right explanation so I invent something different" is not a useful way to learn.

 

[rogerk8]

What is wrong with "free thinking" and trying to understand things your own way?

 

[D H]

I know so little and understands so little so maybe I should quit now?

You should quit speculating and instead try to understand what people have posted.

Anyway here is how I see it: ...
This clearly states that, in the beginning, protons could not have bundled up due to gravity while the electromagnetic force is way much higher (to say the least).

That is precisely the kind of speculating you need to stop doing.

You are ignoring pressure, density, and temperature, and you are also ignoring the fact that the Sun is electrically neutral. The gravitational attraction between two protons is not responsible for fusion. Gravity is far too weak a force to overcome electrical repulsion between two protons. Gravitation is nonetheless absolutely essential. While the gravitational force between two protons is exceedingly small, the mutual gravitational interaction amongst the ~10⁵⁷ 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. The pressure at some point inside the Sun is equal to the weight of all the stuff above that point.

At the center of the Sun, this makes for a pressure of about 250 billion atmospheres, a temperature of about 15 million Kelvin, and a density of about 150 grams/cm³. That density is immense. 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. It is the temperature and density that are ultimately responsible for fusion. The high temperature makes for particles with very high velocities. The high density means *lots* of collisions between those fast moving particles.

 

[Astronuc]

150 grams/cm³ is really impressive as density goes, especially where hydrogen is concerned. That's 150 moles of H/cc, which is ~9 E25 protons/cc, as compared to 1 gm/cc (density of water), or density of air/gas at sea level, or density of a plasma in magnetic confinement, which is on the order of 1e14 H/cc. So the density in the sun's core is about 1e11 to 1e12 times of what we can accomplish in terrestrial systems.

 

[rogerk8]

I thank you all and will comment on your posts individually later in another letter because I haven't slept a single second tonight.

For now, I just want to say this:

I got it!

This morning about 5:30 AM I "woke up" and finally understood the following (in a closed system):

$$E_{tot}=m_pg_sh+\frac{m_pv^2}{2}=m_pg_sh+kT=constant$$

Which means that as h decreases, T increases!

The only minor question I have here is where this Ek=kT comes from. My guess is the Maxwellian velocity distribution where you however can discuss if the distribution is Maxwellian or not.

I have used this energy conservation solution to a complicated problem before. In that case I used it, with your thankful help, to determine the loss of speed for a planet while being submitted to a gravitational sling shot.

It is amazing how often you can use this fundamental law!

Roger
PS
Feel free to correct me if I'm wrong.

 

[rogerk8]

mgh is good enough for the basic idea. You have a large mass of hydrogen in a cube .1 light years on a side. Under the influence of self gravitation, it collapses to a diameter of 1 million miles (appx). That means the average h in mgh, for given volume of hydrogen is about 100 billion miles. The g 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.

What is easy about that, you mean?

Normally, a neutron decays via weak interaction (in about 10 minutes if outside of a nucleus) into proton, an electron, and an anti-neutrino.

Very interesting information. Do I dare ask why? And neutrinos, are those the kind of particles that can't be stopped or registered by almost any means?

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.

I will not ask why, I simply find it interesting. Recognizing that a positron is a positively charged electron.

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).

KE means keV, right? And I have never heard about a blue moon. Totally new to me who watches almost every scientific program on the telly. And yet manage to understand so little Anyway what you seem to say is that the "decays" gives rise to both a proton and a neutron among other fantastic particles and they fuse into deuterium and releases net energy. All of this due to high temperature and high density, right?

Thanks for all your help!

Roger

 

[Astronuc]

KE means keV, right? And I have never heard about a blue moon. Totally new to me who watches almost every scientific program on the telly. And yet manage to understand so little Anyway what you seem to say is that the "decays" gives rise to both a proton and a neutron among other fantastic particles and they fuse into deuterium and releases net energy. All of this due to high temperature and high density, right?

Thanks for all your help!

Roger

KE refers to kinetic energy, and kinetic energy of the atoms/molecules in a gas are related to temperature.

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

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c1

Protons, neutrons and electrons were formed along time ago, back at the origin of the universe.

 

[rogerk8]

You are ignoring pressure, density, and temperature, and you are also ignoring the fact that the Sun is electrically neutral. The gravitational attraction between two protons is not responsible for fusion. Gravity is far too weak a force to overcome electrical repulsion between two protons. Gravitation is nonetheless absolutely essential. While the gravitational force between two protons is exceedingly small, the mutual gravitational interaction amongst the ~10⁵⁷ 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. The pressure at some point inside the Sun is equal to the weight of all the stuff above that point.

1) Very educational!
2) If you read my earlier post you may discover that I have already calculated the Fq/Fg for protons to be 10³⁶ and thus enormous.
3) What has this to do with pressure? To me pressure is nkT.
4) This is very interesting and educational information. I can not really understand it even though it sounds obvious.

At the center of the Sun, this makes for a pressure of about 250 billion atmospheres, a temperature of about 15 million Kelvin, and a density of about 150 grams/cm³. That density is immense. 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. It is the temperature and density that are ultimately responsible for fusion. The high temperature makes for particles with very high velocities. The high density means *lots* of collisions between those fast moving particles.

1) Tells me nothing. It's just a huge number.
2) This is a verification of the figure given for ITER which aims at 10 times the temperature of the Sun for some reason. Feel free to educate me
3) This unfortunatelly also tells me nothing. 150 grams per cubic cm almost sounds tiny to me.
4) This is amazing to say the least! How do I calculate that?
5) Roger that.
6) Incredible good explanation. Thank you!

Roger

 

[rogerk8]

150 grams/cm³ is really impressive as density goes, especially where hydrogen is concerned. That's 150 moles of H/cc, which is ~9 E25 protons/cc, as compared to 1 gm/cc (density of water), or density of air/gas at sea level, or density of a plasma in magnetic confinement, which is on the order of 1e14 H/cc. So the density in the sun's core is about 1e11 to 1e12 times of what we can accomplish in terrestrial systems.

Hi Astronuc!

Above I recently said that I thought 150 grams per cubic cm was almost tiny. I kind of regret that now because I was referring to one cubic cm of something solid. I thus formed my fingers to 1 cm and immagined it to weigh 150 grams. It did actually not sound so impressive coming from the core of the Sun but I kind of forgot the cubic cm being a gas (i.e a plasma)

Take care!

Roger

 

[PAllen]

Hi Astronuc!

Above I recently said that I thought 150 grams per cubic cm was almost tiny. I kind of regret that now because I was referring to one cubic cm of something solid. I thus formed my fingers to 1 cm and immagined it to weigh 150 grams. It did actually not sound so impressive coming from the core of the Sun but I kind of forgot the cubic cm being a gas (i.e a plasma)

Take care!

Roger

It is still 10 times denser than the core of the earth, and also much denser than any terrestrial solid. For example, gold is 19.3 grams / cubic centimeter, lead is 11.3. Note, iron at the surface of the Earth is only 7.9 , but under the pressure in the core, it nearly doubles.

 

[rogerk8]

Amazing!

 

[rogerk8]

It is still 10 times denser than the core of the earth, and also much denser than any terrestrial solid. For example, gold is 19.3 grams / cubic centimeter, lead is 11.3. Note, iron at the surface of the Earth is only 7.9 , but under the pressure in the core, it nearly doubles.

I agree I was very stupid with my estimation. And now that you explain even further I feel even more stupid. Heavy stuff like gold only some 20 grams per cubic cm. 20 grams! And gold is among the most dense material I know. Maybe except for Uranium.

But would you mind explaining the bold part. I simply do not grasp this pressure business.

It also seems like I can't understand that solids can get denser due to pressure.

But by saying this I also kind of understand that they can.

Roger

 

[rogerk8]

By the way, my formula is wrong.

I kind of forgot 1/r^2 in g and more importantly, that h is defined above the surface of the Sun.

Roger

 

[D H]

3) What has this to do with pressure? To me pressure is nkT.

No. Look at the units. Always look at the units! The right hand side has units of energy, not pressure.

The ideal gas law says PV=NRT (chemistry), or PV=nkT (physics). They're the same equation, and in both cases the units are correct. The only difference between the two is whether one uses number of moles or number of molecules. Divide both sides by volume and you'll find that pressure is proportional to the product of density and temperature.

1) Tells me nothing. It's just a huge number.

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.

2) This is a verification of the figure given for ITER which aims at 10 times the temperature of the Sun for some reason. Feel free to educate me

I'll say more about this below.

3) This unfortunatelly also tells me nothing. 150 grams per cubic cm almost sounds tiny to me.

I very specifically said that this is about eight times the density of solid uranium. You even highlighted that phrase! We are trying very hard to make this understandable to you by relating to things with which you might be familiar. That you highlighted, in bold, what I wrote and then had the audacity to write that this "almost sounds tiny to me" is rather annoying. We have spent a good deal of time responding to your queries. You should respond in kind and try to comprehend what we write.



As for why ITER is aiming for a temperature much higher than the 15 million degree temperature at the center of the Sun, I'm going to ask a rhetorical question. Here it is: Per unit volume, what produces more energy, the biological processes in a warm compost pile, or the nuclear fusion at the center of the Sun?

The surprising answer is a warm compost pile.


Almost all of the proton-proton collisions at the energies present in the center of the Sun result in two protons just bouncing off one another. There is no fusion. Only rarely do those collisions result in the production of deuterium. The p-p reaction is by far the slowest link in the p-p chain. On the rare occasion where two protons do combine to form deuterium, the rest of the p-p chain proceeds rather quickly to eventually form helium.

To make fusion worthwhile we have to do a lot (a whole lot) better than creating a very expensive warm compost pile. One way around the problem is to bypass the p-p reaction. That is why ITER is using deuterium and tritium. This is the easiest reaction to create. Even then, the odds are still pretty lousy at 15 million kelvin. Bumping the temperature up an order of magnitude and makes for something that produces a whole lot more energy than a warm compost pile.