Zusammenfassung
Space focusing of a linear time-of-flight mass spectrometer (TOFMS) with an arbitrary number N of ion acceleration regions, a field free drift tube, and a reflectron is analyzed. A quality function Q(d,u(0)) is defined as the fractional error in the flight time of an ion with initial position d and initial velocity u(0) with respect to an ion with d=0 and u(0)=0. This quality function has the ...
Zusammenfassung
Space focusing of a linear time-of-flight mass spectrometer (TOFMS) with an arbitrary number N of ion acceleration regions, a field free drift tube, and a reflectron is analyzed. A quality function Q(d,u(0)) is defined as the fractional error in the flight time of an ion with initial position d and initial velocity u(0) with respect to an ion with d=0 and u(0)=0. This quality function has the form Q(d,u(0))=-u(0)/f(0)+F(u(0)(2)-d), where the function f(y) depends on the dimensions and the field strengths chosen for the instrument, and F(y)=f(y)/f(0)-1. The quality function is optimized up to the order k by setting all Taylor coefficients of F(y) up to and including y(k) equal to zero and solving this system of equations for the design parameters of the instrument. A linear TOFMS with N acceleration regions can be optimized in this way with respect to N design parameters. An additional reflectron will not add another optimizable parameter, i.e., no further Taylor coefficient can be made to vanish. After optimization of the TOFMS with respect to all field strengths including that in the reflectron, the quality function becomes independent of the length of the field free drift tube. Hence, the effect of the reflectron is to make space focusing independent from the drift tube length. The quality function for a fully optimized TOFMS depends only on the number N of acceleration stages and is, for a given N, identical for the designs with and without a reflectron. However, the design containing a reflectron has a smaller value of the factor 1/f(0) which determines the error introduced by the initial velocity distribution of the ions. A space focused TOFMS cannot be further focused with respect to the initial velocity u(0), since the first term in the Taylor expansion of the quality function in the variable u(0) is proportional to the inverse of the total flight time. For a TOFMS with two or more acceleration regions this is the dominant source of error that remains after space focusing. This situation cannot be improved by delayed or pulsed extraction of the ions from the ionization region nor by deceleration of the ions before they enter the field free region. (C) 2000 American Institute of Physics. [S0034-6748(00)03412-2].
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