Optimization of a one-dimensional time-of-flight mass spectrometer

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, a nd 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 qual ity function has the form Q(d,u(0))=-u(0)/f(0)+F(u(0)(2)-d), where the func tion 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 t he 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 param eters of the instrument. A linear TOFMS with N acceleration regions can be optimized in this way with respect to N design parameters. An additional re flectron will not add another optimizable parameter, i.e., no further Taylo r coefficient can be made to vanish. After optimization of the TOFMS with r espect to all field strengths including that in the reflectron, the quality function becomes independent of the length of the field free drift tube. H ence, the effect of the reflectron is to make space focusing independent fr om 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 desig n containing a reflectron has a smaller value of the factor 1/f(0) which de termines the error introduced by the initial velocity distribution of the i ons. A space focused TOFMS cannot be further focused with respect to the in itial velocity u(0), since the first term in the Taylor expansion of the qu ality function in the variable u(0) is proportional to the inverse of the t otal flight time. For a TOFMS with two or more acceleration regions this is the dominant source of error that remains after space focusing. This situa tion cannot be improved by delayed or pulsed extraction of the ions from th e ionization region nor by deceleration of the ions before they enter the f ield free region. (C) 2000 American Institute of Physics. [S0034-6748(00)03 412-2].