Problem 3 discusses the + 11 charge state of 129 Xe leaving the source under a v

Question

Problem 3 discusses the + 11 charge state of 129 Xe leaving the source under a voltage of 10 kV. After selecting this beam, we later accelerate it to 24.8 MeV/u out of the cyclotron with a measured output current of 1.25 nA (defined in the usual way except the charge carriers are +11 Xe ions instead of electrons, and the drift velocity is the velocity associated with the ion energy) (a) how many Xe ions per second leave the cyclotron? (b) How much power does this beam carry (this is important to figure out how much heat it deposits on a target)

Explanation / Answer

VOltage, V = 10,000 V
charge, q = +11e
mass = m = 129u

final energy, E = 24.8 MeV/u
Final measured current,i = 1.25 nA

a) i = 1.25 nA
per unit time charge, q = i*t = i*1 = 1.25 nC
so, number of xenon atoms = n
so, n*11e = 1.25 nC
n*11*1.6*10^-19 = 1.25*10^-9
n = 7.10227*10^8 atoms/sec
b) Final energy, U = E*m = 24.8*10^6*129 eV ( per atom )
Final power = n*U eV/s = 2.272159*10^18 eV = 0.363 W

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