λ obs ¼ λ s
ffiffiffiffiffiffi
cþν
cÀν
q
, where λ s is the wavelength for a stationary observer, c is the speed of
light, and v is the speed of the ions. As the ions travel with a speed of 10
5 m/s, which
is much less than the speed of light, λ obs % λ s .
0.0
0.2
0.4
0.6
0.8
1.0
0
2
4
6
8
y = A 1 exp(-t/t 1 ) + A 2 exp(-t/t 2 )
Counts / 1000
a
b
0
2
4
6
8
10
Revolution time
is 100 ms
Time 0 is when the laser is fired
First data point measured at 50 ms
Time (ms)
Fig. 3.6 (a) Illustration to show that while the first data point in a time spectrum measured at
ELISA is measured after half a revolution in the ring, the data can be fit to determine the total
number of photoexcited ions: To describe the data collected at ELISA a set of exponentials are fit
to the lifetime data, e.g. for two exponentials; y ¼ A 1 exp(Àt/τ 1 ) + A 2 exp(Àt/τ 2 ), where the first
term relates to the photoexcited ions which decay with a time constant τ 1 and the second term with
a time constant τ 2 accounts for CID decay (τ 2 ) τ 1 ). From these fits, it is possible to calculate a
number proportional to the total number of photoexcited ions, N Ions,1
*
¼ A 1 τ 1 and absorption cross
sections can be calculated using the following formula: Abs 1 ¼ A 1 τ 1 /(N Background (N Photons )
x
),
where N Background is the neutrals signal arising from CID prior to photoexcitation, which is
proportional to the number of ions in the beam, and is included to account for variations in the
ion-beam intensity; N Photons is the number of photons in the laser pulse; and x is either 1 or 2 for
one- or two-photon absorption, respectively. (b) The fit from (a), along with each of the constituent
exponentials
26
J.A. Wyer
ffiffiffiffiffiffi
cþν
cÀν
q
, where λ s is the wavelength for a stationary observer, c is the speed of
light, and v is the speed of the ions. As the ions travel with a speed of 10
5 m/s, which
is much less than the speed of light, λ obs % λ s .
0.0
0.2
0.4
0.6
0.8
1.0
0
2
4
6
8
y = A 1 exp(-t/t 1 ) + A 2 exp(-t/t 2 )
Counts / 1000
a
b
0
2
4
6
8
10
Revolution time
is 100 ms
Time 0 is when the laser is fired
First data point measured at 50 ms
Time (ms)
Fig. 3.6 (a) Illustration to show that while the first data point in a time spectrum measured at
ELISA is measured after half a revolution in the ring, the data can be fit to determine the total
number of photoexcited ions: To describe the data collected at ELISA a set of exponentials are fit
to the lifetime data, e.g. for two exponentials; y ¼ A 1 exp(Àt/τ 1 ) + A 2 exp(Àt/τ 2 ), where the first
term relates to the photoexcited ions which decay with a time constant τ 1 and the second term with
a time constant τ 2 accounts for CID decay (τ 2 ) τ 1 ). From these fits, it is possible to calculate a
number proportional to the total number of photoexcited ions, N Ions,1
*
¼ A 1 τ 1 and absorption cross
sections can be calculated using the following formula: Abs 1 ¼ A 1 τ 1 /(N Background (N Photons )
x
),
where N Background is the neutrals signal arising from CID prior to photoexcitation, which is
proportional to the number of ions in the beam, and is included to account for variations in the
ion-beam intensity; N Photons is the number of photons in the laser pulse; and x is either 1 or 2 for
one- or two-photon absorption, respectively. (b) The fit from (a), along with each of the constituent
exponentials
26
J.A. Wyer