The future of particle accelerators

I ran some calculation for a hypothetical Tau particle accelerator as follows:

I had to assume an extremely high as yet unobtainable potential gradient of 300,000,000 GeV/km or 300,000 TeV/km. However, perhaps with novel types of accelerators perhaps including accelerators that use modulated visible light or higher frequency laser light to drive the particles, such accelerators can be built.

For E = 1 TeV, I calculated tau = [(MoC)/(qe)] ln [(2E)/[(Mo)[C EXP 2]]] = {{(1.77684 GeV)/[[ (3 x 10 EXP 5) km/second] EXP 2]}[( 3 x 10 EXP 5) km/second]/[(300,000,000 GeV/km)]} ln {[ 2,000 GeV]/[1.77684 GeV]} = (1.974267 x 10 EXP -14) ln {[ 2,000 GeV]/[1.77684 GeV]} = 1.387132 x 10 EXP – 13.

Now the half life of the Tauon = 2.9 x 10 EXP – 13 seconds.

Therefor the percentage of Tauons surviving was calculated as 2 EXP {-[1.387132 x 10 EXP – 13]/[ 2.9 x 10 EXP – 13]} = 71.78 %

The required Linac length would be 1 TeV/[300,000 TeV/km] = 0.0033 meters

Next I ran the calculations for E = 10 TeV or 20,000 GeV.

For tau, the math is as follows.

tau = [(MoC)/(qe)] ln [(2E)/[(Mo)[C EXP 2]]] = {{(1.77684 GeV)/[[ (3 x 10 EXP 5) km/second] EXP 2]}[( 3 x 10 EXP 5) km/second]/[(300,000,000 GeV/km)]} ln {[ 20,000 GeV]/[1.77684 GeV]} = (1.974267 x 10 EXP -14) ln {[ 20,000 GeV]/[1.77684 GeV]} = 1.84172 x 10 EXP – 13.

The surviving percentage of Tauons is 2 EXP {-[1.84172 x 10 EXP – 13]/[ 2.9 x 10 EXP – 13]} = 64.39 percent. The length of the linac would be 10 TeV/ [300,000 TeV/km] = 0.033 meters.

Next, I ran the calculations for 100 TeV or 100,000 GeV Tauons also with a gradient of electrical potential of 300,000 TeV/km.

For tau, the math is as follows.

tau = [(MoC)/(qe)] ln [(2E)/[(Mo)[C EXP 2]]] = {{(1.77684 GeV)/[[ (3 x 10 EXP 5) km/second] EXP 2]}[( 3 x 10 EXP 5) km/second]/[(300,000,000 GeV/km)]} ln {[ 200,000 GeV]/[1.77684 GeV]} = (1.974267 x 10 EXP -14) ln {[ 200,000 GeV]/[1.77684 GeV]} = 2.2963 x 10 EXP – 13 seconds.

The surviving percentage of Tauons is 2 EXP {-[2.2963 x 10 EXP – 13]/[ 2.9 x 10 EXP – 13]} = 57.76 percent. The length of the linac would be 100 TeV/ [300,000 TeV/km] = 0.333 meters.

Next, I ran the calculations for 1,000 TeV or 1,000,000 GeV Tauons also with a gradient of electrical potential of 300,000 TeV/km.

For tau, the math is as follows.

tau = [(MoC)/(qe)] ln [(2E)/[(Mo)[C EXP 2]]] = {{(1.77684 GeV)/[[ (3 x 10 EXP 5) km/second] EXP 2]}[( 3 x 10 EXP 5) km/second]/[(300,000,000 GeV/km)]} ln {[ 2,000,000 GeV]/[1.77684 GeV]} = (1.974267 x 10 EXP -14) ln {[ 200,000 GeV]/[1.77684 GeV]} = 2.7509 x 10 EXP – 13 seconds.

The surviving percentage of Tauons is 2 EXP {-[2.7509 x 10 EXP – 13]/[ 2.9 x 10 EXP – 13]} = 51.81 percent. The length of the linac would be 1,000 TeV/ [300,000 TeV/km] = 3.333 meters.

I went further still and ran the calculations for 1,000,000 TeV Tauons also with a gradient of electrical potential of 300,000 TeV/km.

For tau, the math is as follows.

tau = [(MoC)/(qe)] ln [(2E)/[(Mo)[C EXP 2]]] = {{(1.77684 GeV)/[[ (3 x 10 EXP 5) km/second] EXP 2]}[( 3 x 10 EXP 5) km/second]/[(300,000,000 GeV/km)]} ln {[ 2,000,000,000 GeV]/[1.77684 GeV]} = (1.974267 x 10 EXP -14) ln {[ 2,000,000,000 GeV]/[1.77684 GeV]} = 4.11469 x 10 EXP – 13 seconds.

The surviving percentage of Tauons is 2 EXP {-[4.11469 x 10 EXP – 13]/[ 2.9 x 10 EXP – 13]} = 37.4 percent. The length of the linac would be 1,000,000 TeV/ [300,000 TeV/km] = 3,333 meters or 3.3 km.

Obviously, a way to create sufficient quantities of Tauons in a small region simultaneously, the ability to collate them, to accelerate them quickly to the point were relativistic time dilation would effectively greatly increase their lifetimes, and a way to filter out noise from random tauon decays within or near the vicinity of the systems detectors would need to be worked out.

Note that I ran similar calculations for a whole host of electrically charged mesons and baryons, such as are comprised of strange quarks, charmed quarks and/or bottom quarks, and derived similar results. In short I have run the numbers and scenarios for about a few dozen such particle species for particles with non-relativistic mean half lives of any where from about 10 EXP - 8 seconds to as small as about 10 EXP - 14 seconds.

I can provide the numbers in these later scenarios, some of which can in theory be realized with significantly smaller acceleration potential than the case of the Tauons given above.