# Theoretical Study of High-Order Velocity Focusing Achieved with Single-Stage Reflectron Time-of-Flight Mass Spectrometry

## TL;DR

This paper shows that a single-stage reflectron time-of-flight mass spectrometer can achieve high-order velocity focusing, challenging previous assumptions about the need for multiple stages.

## Contribution

The study introduces a new model showing that second-order velocity focusing can be achieved with a single-stage reflectron using optimal parameters.

## Key findings

- A single-stage reflectron can achieve second-order velocity focusing with optimal parameters.
- Delayed extraction is more effective than reflectors for compensating initial ion velocity spread.
- The model predicts a maximum mass resolving power of 750,000 for ions with m/z of 10,000.

## Abstract

This study explores unexplained fundamental principles
of reflectron
time-of-flight (R-TOF) mass spectrometry (MS). Conventional calculations
focusing on the ion trajectory in reflectors concluded that multistage
reflectors are necessary to achieve second-order velocity focusing
at ion detectors. This study demonstrates that in an instrument equipped
with a matrix-assisted laser desorption/ionization (MALDI) ion source
a single-stage reflector can achieve second-order velocity focusing
when the optimal experimental parameters predicted using the coupled
space and velocity focusing (CSVF) principle are used. The optimization
model indicates that the delayed extraction technique is more effective
in compensating for the initial ion velocity spread than reflectors.
The calculation shows that for ions with m/z of 10,000, the predicted maximum mass resolving power
(R

m
) can reach 750,000
using a single-stage R-TOF MS with an effective total length of about
2.4 m, or approximately 130,000 when accounting for the temporal response
limit of ion detectors. The calculation model also reveals that in
second-order focusing conditions, ions have two focusing points along
the flight path, instead of just one at the detector as conventionally
believed. The result indicates that the new model is critically important
for the advancement of R-TOF MS.