Colliding protons and electrons and making them fuse, Gravitational energy density, and scale

The Slow Mo Guys: Ridiculous Magnets Colliding at 187,000FPS – The Slow Mo Guys at https://www.youtube.com/watch?v=yHPtuEfMPTc

Slow Mo Guys, you can do the same with protons, electrons, positrons, anti-protons, any particle with a permanent magnetic dipole moment. You have to line up the spins properly, and time them using magnetic resonant imaging methods. But it can be done very very precisely with not a lot of equipment. For “Tabletop fusion” pulsed magnetic gradients from lasers can be used to accelerate and align the atomic particle magnets.

The magnetic field of a particle magnetic dipole is a vector calculation. You find the details at Wikipedia under “Magnetic dipole force” and related articles.

If you line up the protons so they point North, for instance, and send a beam from the south and a beam from the North, when they get closer their north and south will be attractive. The equation for the magnetic field is

B(r) = μ₀*mup/(2*π* r³)

Mu0 is the vacuum magnetic permeability. The Codata value is 1.25663706212E-6 Newtons/Ampere^2
Mup is the Cocata proton magnetic moment. Mup = 1.41060679736E-26 Joules/Tesla

B(r = 1 picoMeter) = (1.25663706212E-6) * (1.41060679736E-26)/ (2* pi* (1E-12)^3

B(r – 1 pm) = 2821.21359626 Tesla or 2.82121359626 KiloTesla

Parallel to the proton, where it is pointed North and traveling North-South, and 1 picometer way, the field will be half or 1.41060679813 KiloTesla

But hitting the protons head on is going to be a bit iffy.at first. What is likely to happen is they will just miss and only at near collisions will they hit and stick.

But I think that is mostly a matter of iterative learning. Using magnetically aligned and precisely tuned proton beams is going to narrow the collision conditions a lot. You are not randomly hitting hot protons pointing in many directions and all on their own schedule and paths, but keeping them to precise paths and times and energies.

The energy density is calculated

MagneticEnergyDensity = B²/(2*μ₀)

(1410.60679813 Tesla)² / (2 * 1.25663706212E-6 Tesla*meter/Ampere) gives a value of

7.91720855E11 Pascals or 791.720855 GigaPascal

(2821.21359626 Tesla)² / (2 * 1.25663706212E-6 Tesla*meter/Ampere) gives a value of

3.16688342E12 Pascals or 3.16688342 TeraPascal

I use the full precision, so that anyone can trace the calculation. The floating point calculations are usually at least this good and so always use the latest and best Codata, and not round off. If you round or guess, the Internet gets filled up with partial and incomplete calculations and examples that are a mess to clean up. Do it right, do it once and for everyone on the Internet.

If we can get the “best calculations” and models and data share globally on the Internet, then we all can just use the master equations, and not have to make billions of copies, with the usual human and AI mistakes and omissions.

For the electron at 1 nanometer

B = (1.25663706212E-6 T*m/A) * (9.2847647043E-24 J/T) / (2 * π * (1E-9 m)³) = 1.85695294187 Tesla
U = (1.85695294187 Tesla)² / (2 * 1.25663706212E-6 Tesla*meter/Ampere) = 271.7586623 MegaPascal

The gravitational energy density has not been calibrated, it depends on frequency, on the spectrum of fluctuations. Roughly

U_B = B² / (2 * μ₀)

U_g = g^2/(8*pi*G)

B = g*sqrt(μ₀/(4*pi*G))

sqrt((1.25663706212E-6) / (4 *pi * 6.67430E-11)) = 38.7076796657 Telsa/(meter/second^2)) = 38.7076796657 Tesla/(meter/second²)

B = (9.8 m/s^2) * 38.7076796657 Tesla/(meter/second²) = 379.335260724 Telsa  comparable in energy density to the earths gravitational field.

r^3 = (Mue/g)*sqrt(mu0*G/pi)

sqrt(mu0*G/pi) = sqrt(1.25663706212E-6*6.67430E-11/pi) = 5.16693333e-9 { check units }

r = [ (9.2847647043E-24)*5.16693333e-9/(9.8) ]^(1/3)

r = 1.6979539e-11 meters = 16.979539 picoMeters = 16979.539 nanometers

E_Joules = h*nu/lambda = PlancksConstant*SpeedLightGravity/WaveLength

E_ElectronVolts = E_Joules*ElectronCharge
E_ElectronVolts = (PlancksConstant*SpeedLightGravity*ElectronCharge)/WaveLength

(PlancksConstant*SpeedLightGravity/ElectronCharge) = (6.62607015E-34 Joules/Hertz)*(2.99792458E8 Meters/second)*(1.602176634E-19 Coulombs) = 1239.84198433E-9 ElectronVolt*nanoMeters

E_ElectronVolts = (1.23984198433E-6 )/(16.979539e-12) = 73.0197671639 KeV The energy of a photon with wavelength 16.979539 picoMeters. But the important parameter is the volume integral of the magnetic energy density, and the spectrum of magnetic fluctuations from which the large scale gravitational effect emerge.  The gravitational acceleration is just an acceleration, and that is tied to the force.

nanometers and picosecond for protons
picometers and picoseconds for electrons

Richard Collins, The Internet Foundation