How Electric and Magnetic Fields work in Mass Specs

Electric fields and magnetics field act differently on particles:

Assume we will shoot ions at high speed through a field and separate them: All will have same energy, e.g., 10keV

But this means different velocities because E = 1/2mv2

1. Magnetic Fields Sort Ions according to mass:

Magnetic force = B e v, where B = field, e = charge, v = veloc. So force α veloc.

Compare Hydrogen and Deuterium:

Veloc. of H is 2 times greater (kinetic E = 1/2mv2)

Force on H is 2 times greater

Acceleration (a=F/m), 2 2 times greater (it’s 1/2 the mass)

But, greater v means less time in the field (factor of 2 ) And Displacement α t2, so this means 1/2 the displacement

Net effect: Displacement is 2 greater for H+ than for D+. Conclusion: Ions in a mag. field have circular paths:

￼￼￼￼￼￼￼￼￼m −5 B2r2

e = 4.825 ×10 units of e- charges))

V (B = mag field (Gauss), V = accel. voltage, e is charge (in integer

￼￼

r2 α kinetic energy α veloc.2

r2 α mass

**Note that an ion with 2 times the mass and a double charge will follow the same path.

2. Electric fields sort ions according to kinetic energy alone:

Force depends on charge alone: Same force for H and D H accel. = 2 D accel.

Time in field: 2 times greater for D than for H But displacement = at2

Therefore: the greater time and slower accel. for D cancel out.

Conclusion: In an electric field, all ions with same velocity/energy take the same path. Electric fields can be used as “energy filters”

r = 2E (r = path radius, E = energy of ions, V = field voltage) Vsector

Utility: Collisions in imperfect vacuum slowed ions (need to filter out)