pressure
pressure
How much force is required to fuse 2 deuterium ions together? I calculated something like .1 newtons but that seems awfully high for two particles that are so small...
Re: pressure
Did you take tunneling into account?
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prestonbarrows
- Posts: 78
- Joined: Sat Aug 03, 2013 4:41 pm
Re: pressure
Pressure in the classical sense does not really apply to individual fusion reactions. Each time two particles collide, they have a certain probability of fusing. That probability (cross section) is dependent on which elements they are and their relative energies (velocities).
For fusion reactions, you typically need energies on the order of keV but the Coulomb repulsion is on the order of MeV. Classically, fusion reactions could almost never happen. In reality, almost all fusion happens due to quantum tunneling through this barrier. This is where the probabilistic nature comes in.
For fusion reactions, you typically need energies on the order of keV but the Coulomb repulsion is on the order of MeV. Classically, fusion reactions could almost never happen. In reality, almost all fusion happens due to quantum tunneling through this barrier. This is where the probabilistic nature comes in.
Re: pressure
Good answers, but just to confound the issue with my perspective. ...
The density/ pressure does not effect the probability of fusion between two selected particles. The velocity, the coulomb barrier and quantum tunneling is probably the only real considerations.
Where pressure or density comes into play is consideration of the number of particles and thus the total number of collisions occurring per unit of time. The small percentage of collisions that results in fusions stays the same. This number of total collisions scale as the square of the density and the fusion subset increases at the same rate- at least with beam- beam fusion. Beam- target or beam- background fusion may not scale quite the same. Also, as with beam- beam considerations (only 1/2 the velocity relative to the lab frame of reference is needed (or is that 1/2 the KE?)) and the resultant pressure versus fusion rate would reflect this.
The nature of the plasma may contribute also. Monoenergetic versus thermal distribution may apply. Also, density distribution with any location may change compared to the average density. Are there gradients? If the Polywell or other schemes have confluence towards a location such as the center of a quasispherical sphere the density changes, perhaps profoundly, such that the majority of fusions (and total collisions) occur in a small volume subset of the total. In the EMC2 Patent application this plays a role in the high fusion rate of converging ions that is governed by a relatively low confining electron pressure. At the center the ion velocities are large, but at the periphery the ion velocities are low- thus the pressure is relatively low, and it is this pressure that the electron density on the edge needs to confine- and resultant pressure that the magnetic confinement needs to withstand.
In some systems the density may actually influence fusion rates directly, such that particles are so densly packed together that they will collide so often that they cannot escape the dense volume without fusing. This is mentioned in the EMC2 patent again as a theoretic but unrealistic possibility. It might apply in some natural situations as well such as on the surface of White dwarf or neutron stars. Essentially this is inertial confinement fusion like bombs. To a lesser extent such also happens in the cores of lighter main sequence stars such as the Sun. The fusion probabilities (the P-P cross section is stupendously low), but because of the high density, not to mention the large volumes, prodigious amounts of fusion proceeds. Still, I think this is basically a product of velocity considerations, quantum tunneling, and time. The true change where pressure directly dictates the probabilities may be the interior of Neutron stars where the density/ pressure is so great that the protons and electrons are squeezed into a big ball of neutrons. This is of course driven by gravity, which is not an issue in normal situations.
Dan Tibbets
The density/ pressure does not effect the probability of fusion between two selected particles. The velocity, the coulomb barrier and quantum tunneling is probably the only real considerations.
Where pressure or density comes into play is consideration of the number of particles and thus the total number of collisions occurring per unit of time. The small percentage of collisions that results in fusions stays the same. This number of total collisions scale as the square of the density and the fusion subset increases at the same rate- at least with beam- beam fusion. Beam- target or beam- background fusion may not scale quite the same. Also, as with beam- beam considerations (only 1/2 the velocity relative to the lab frame of reference is needed (or is that 1/2 the KE?)) and the resultant pressure versus fusion rate would reflect this.
The nature of the plasma may contribute also. Monoenergetic versus thermal distribution may apply. Also, density distribution with any location may change compared to the average density. Are there gradients? If the Polywell or other schemes have confluence towards a location such as the center of a quasispherical sphere the density changes, perhaps profoundly, such that the majority of fusions (and total collisions) occur in a small volume subset of the total. In the EMC2 Patent application this plays a role in the high fusion rate of converging ions that is governed by a relatively low confining electron pressure. At the center the ion velocities are large, but at the periphery the ion velocities are low- thus the pressure is relatively low, and it is this pressure that the electron density on the edge needs to confine- and resultant pressure that the magnetic confinement needs to withstand.
In some systems the density may actually influence fusion rates directly, such that particles are so densly packed together that they will collide so often that they cannot escape the dense volume without fusing. This is mentioned in the EMC2 patent again as a theoretic but unrealistic possibility. It might apply in some natural situations as well such as on the surface of White dwarf or neutron stars. Essentially this is inertial confinement fusion like bombs. To a lesser extent such also happens in the cores of lighter main sequence stars such as the Sun. The fusion probabilities (the P-P cross section is stupendously low), but because of the high density, not to mention the large volumes, prodigious amounts of fusion proceeds. Still, I think this is basically a product of velocity considerations, quantum tunneling, and time. The true change where pressure directly dictates the probabilities may be the interior of Neutron stars where the density/ pressure is so great that the protons and electrons are squeezed into a big ball of neutrons. This is of course driven by gravity, which is not an issue in normal situations.
Dan Tibbets
To error is human... and I'm very human.