lon Source Particle Beam Weapon - You have received a DARPA contract to design a

Question

lon Source Particle Beam Weapon - You have received a DARPA contract to design an anti-satellite particle beam weapon due to your knowledge of ion sources learned in PHYS 1112K. Instead of being mounted horizontally, you will mount the ion source vertically as shown below. Assume you choose a beam of protons for your particle beam (see eqn sheet for charge and mass). You want the velocty of the particle beam to be 1/10 the speed of light (c 3.00 x 108 m/s). What voltage is needed for the power supply for your weapon? Note: since c 3.00 x 108 m/s; 1/10c 3.00 x 107 m/s

Explanation / Answer

proton mass, m = 1.6*10^-27 kg

charge, q = 1.6*10^-19 C

v = 0.1c

c = 3*10^8 m/s

B = 26.8 T

a. let electric field be E

then

qvB = qE + mg

E = (qvB -mg)/q = vB - mg/q

E = 804000000 - 0.0000000981 = 803999999.9999999019 V/m

b. d = 0.15 cm

di = 0.2 cm

hence

E = Vi/di = V/d

803999999.9999999019 = V/0.15*10^-2

V = 1205999.999999999852 V

c. B = 26.8 T

wodth = 2r

now

mv^2/r = qvB

hence

mv/r = qB

r = mv/qB

hence

2r = 2mv/qB = 2.23880597 cm

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