Ⅱ-9. Instrumentation

RIKEN Accel. Prog. Rep. 53

Eliminating mass-dependent inaccuracies in MRTOF-MS for the studyof RI using arbitrary reference masses

In high-precision mass spectrometry of radioactive
isotopes, mass dependent inaccuracies are one of themajor topics to be discussed, because the ionic mass
(mass-to-charge ratio) of the rare isotopes to be studied can be distant from that of the reference ionsused for calibration. In Penning-trap mass spectrometry, such eﬀects have been studied extensively inthe past using carbon cluster sources.1) For multireﬂection time-of-ﬂight (MRTOF) mass spectrometry
similar investigations are awaited, but are not completed yet. Other than in Penning traps, in electrostatic ion optics systems the trajectory of ions of equal
energy but diﬀerent mass is exactly the same, whichcomes from fundamental theorems. Following that,√ thedetected TOF of any ion is obtained by tD = α m/q,with the characteristic device constant α and m, q as
mass and charge. The mass can be calculated by useof a reference ion with m1 , q1 and TOF tD1 by:()2
m1 tD − t0,(1)m=qq1 tD1 − t0

relative mass deviation (mcalc − mreal )/mreal

M. Rosenbusch,∗1 P. Schury,∗1 M. Wada,∗1 S. Iimura,∗2,∗3 Y. Ito,∗4 and H. Wollnik∗5with t0 being the oﬀset time of the measurement (startof the TDC). However, mass-dependent inaccuracies
can come from the acceleration process of the ions,which has been investigated in a new theoretical framework.2) The acceleration process of ions out of an ion
trap happens with an electric ﬁeld that is switched onwith a transient in time with duration tT , and induces
a mass-dependent dynamic process. We have found asolution to include such a ﬁeld transition, and to calibrate masses far away from the reference mass despite
this eﬀect, while having only one reference ion species
available during the online measurement. To this end,
the system can be pre-calibrated once using two stable
ion species before the online
according√ measurement√to the new equation tD = α m/q + β q/m having asecond device constant β. During the online measurement, only one of the two reference species serves again
as reference ion. Using a linear approximation of the⃗ =E⃗ max t , aacceleration ﬁeld during the increase EtT
new equation has been found for the mass of the ions:
2
�()2
��′′
�
t �tD1tD1β
t �
�
−  .
(2)m = q D ′ +� D ′��
2α tD1
2α tD1α
∗1
∗2
∗3
∗4
∗5

Wako Nuclear Science Center (WNSC), IPNS, KEK
RIKEN Nishina Center
Osaka University
Advanced Science Research Center, JAEA Ibaraki
Department of Chemistry and Biochemistry, New Mexico
State University- 127 -a)

1.5e-031.0e-035.0e-04
0.0e+00-5.0e-04-1.0e-03-1.5e-03

single-ref. A = 85, uncorrected

3.0e-07b)

2.0e-071.0e-070.0e+00
single-ref. A = 85, corrected-1.0e-0750

100

150200250

ionic mass / u

Fig. 1. Relative deviation from the real mass value (uponrecalculation of the mass from the TOF data of thereﬂectron simulation) as a function of the mass number,using a transition time of 100 ns. a): Recalculationof masses using the usual approach without correction
with mass A = 85 as reference ions. b): Recalculation
with correction using Eq. (2). Note the diﬀerent scales.

The times �t′D , �t′D1 , and �tD1 are reduced detection timesof the radioactive ion, the reference ion online, and thereference ion before the measurement, respectively. Alltimes are reduced according to �t′D = t′D − t2T −t0 , wheretT /2 is a new correction for the switching transition
emerging from the calculations. A simulation model
for a simple TOF mass spectrometer with short TOF ofonly about 40 µs and a long switching time tT = 100 ns
has been written to show ampliﬁed eﬀects. The TOFof ions has been simulated including dynamic acceleration, and over a broad mass range while assuming that
our reference ions have mass A = 85. The results using
the mass equation of the electrostatic problem and the
newly derived mass formula is shown in Fig. 1. It canbe seen that, in our constructed example, the impact ofsuch dynamic ion acceleration can be very signiﬁcant if
the switching is not fully considered. For MRTOF-MS,
however, this eﬀect is usually very small because of thefast switches (20 ns) and the very long TOF of 6 ms.
It will become important for measurements of superheavy nuclei with large mass distances of reference tothe SHE mass (depending on charge state), where theeﬀects can become signiﬁcant. The masses can thenbe accurately derived using the new correction.
References

1) A. Kellerbauer et al., Eur. Phys. J. D 22, 53 (2003).
2) M. Rosenbusch et al., Int. J. Mass Spectrom., underreview (2020).