AN54 Application Note Appendix A

The Effect of Delayed Extraction Jitter on Flight Time Jitter in MALDI TOF-MS

an54pic.jpg (10998 bytes)

Figure 1. A simplified representation of a MALDI TOF-MS with delayed extraction implemented by pulsing the voltage on the sample holder.

In figure 1, the accelerating voltage on the sample holder is zero volts at the time of the Laser pulse. The Laser pulse causes desorption and ionization of the molecules of mass, m, with charge, z, and initial velocity, v₀. After an extraction delay time, t , the accelerating voltage on the sample holder is abruptly switched to +U volts. In the time t the individual ion has traveled a distance (1 – f )d towards the grounded grid, where

f = 1 – ( v₀ t / d ) (1)

Consequently, the ion is accelerated through a voltage fU and a distance fd. The change in kinetic energy for the ion is zfU. In other words,

m ( v_D² – v₀² ) / 2 = z f U (2)

Rearranging equation (2) yields the final velocity after acceleration,

v_D = [ v₀² + ( 2 z f U / m ) ]^1/2(3)

Starting with the accelerating force on the ion described by

F = z U / d = m dv/dt (4)

rearranging and integrated from v₀ to v_Dleads to the time in the accelerating field being defined by

t_accel = ( v_D – v₀ ) m d / ( z U ) (5)

The flight time through the field-free drift region of length D is given by

t_drift = D / v_D (6)

The total flight time from the onset of the delayed extraction voltage pulse to the arrival of the ion at the detector is

t = t_accel + t_drift
= [ ( v_D – v₀ ) m d / ( z U ) ] + [ D / v_D ] (7)

To find the jitter in t_accel caused by the full-width-at-half-maximum (FWHM) spread in the initial velocities, D v₀, differentiate equation (5) with respect to v₀. The result is

D v₀ ( dt_accel/dv₀ ) = -K t D v₀ / v_D= D t_{accel, v0}(8)

where

K = 1 + [ ( v_D – v₀ ) m d / ( z U t ) ] (9)

Note that K is always greater than 1.

Now differentiate equation (5) with respect to t to determine the jitter in the acceleration time caused by the jitter D t in t . The result is

D t ( dt_accel/dt ) = -v₀ D t / v_D= D t_{accel, t}(10)

Divide equation (8) by equation (10) to find the relative importance of the velocity spread compared to the extraction delay jitter. The result is

D t_{accel, v0} / D t_{accel, t} = K ( D v₀ / v₀ ) / ( D t / t ) > ( D v₀ / v₀ ) / ( D t / t ) (11)

This same procedure can be repeated for equation (6) to get

D t_{drift, v0} = D v₀ ( dt_drift/dv₀ ) = D v₀ D { [ ( z U t ) / ( m d ) ] – v₀ } / v_D³       (12)
D t_{drift, t}= D t D [ ( z U v₀ ) / ( m d ) ] / v_D³      (13)
D t_{drift, v0} / D t_{drift,
t}= a ( D v₀ / v₀ ) / ( D t / t )      (14)

where

a = 1 – [ ( v₀ m d ) / ( t z U ) ] (15)

Typically,

v₀ ~ 300 m/s t > 180 ns
m ~ 10^-23 kg z = 1.6 x 10^-19 Coulombs (16)
d ~ 0.02 m U ~ 20,000 Volts

Consequently,

( v₀ m d ) / ( t z U ) ~ 0.1 (17)

and

a ť 1 (18)

Therefore,

D t_{drift, v0} / D t_{drift, t}ť ( D v₀ / v₀ ) / ( D t / t ) (19)

As can be noted from equations (11) and (19) the contribution of the delayed extraction jitter to the flight time jitter will be negligible compared to the contribution from the initial velocity spread if

( D v₀ / v₀ ) / ( D t / t ) ť 1 (20)

Normally, the condition in equation (20) will be satisfied, because D v₀ / v₀ is typically of the order of 1, whereas D t = 32 ns for the FASTFLIGHT^TM, and t > 180 ns, ( D t / t ť 1/6 ). Consequently, the timing jitter from FASTFLIGHT makes a negligible contribution to the flight time jitter as noted in application note AN54.


		Home \| Applications \| Contact Us
		Products \| Service \| Training