# MI-0294 

**Slip Stacking at Low Intensity -- Status of the Beam Studies**

## Kiyomi Koba

### February 03 03

**Abstract**

We have started beam studies for 'slip stacking' in Main Injector(MI) in
order to increase proton intensity for anti-proton production. It has
been verified that the system for slip stacking works for a low
intensity beam. Although no beam loss was observed, there was an
unexpected longitudinal emittance growth.

**1. Introduction**

For slip stacking, we use three different rf systems and follow four
steps. Step 1: The first bunch train is injected from the Booster on the
central orbit and captured by the first rf system. To make a room for
the second bunch train, the first bunch train is then decelerated until
it circulates on the inside of the central orbit. Step 2: The second
bunch train is injected on the central orbit and captured by the second
rf system. Step 3: As the two bunch trains have slightly different
energies, they can move relative to each other. Step 4: When the two
bunch trains coincide at the same longitudinal location, they are
captured by the third rf system.

Beam studies of the slip stacking process have started and we have
already established that the stacking procedure works as expected.
Frequency separation and Booster bunch rotation studies were also done
to allow us minimize the longitudinal emittance at recapture.

# 

**2. Momentum aperture scan**

Since two bunch trains have different energies, MI must have an enough
momentum aperture to accept both. The momentum aperture of MI is +/-0.7%
at injection, Fig. 1, corresponding to the frequency separation of
+/-3000Hz from the central value of 52.8114MHz.

![](media/image1.jpeg){width="6.0in" height="5.088888888888889in"}

Figure 1. Momentum aperture scan at MI injection. Beam loss ratio as a
function of momentum spread.

**3. Frequency separation**

Since there are two rf voltages during stacking, they act on both bunch
trains. The bunch shape has been measured to demonstrate that the
frequency separation between the first and the second rf systems is
adequate.

In this measurement, one bunch train was injected, then two rf voltages
were raised and the frequency separation was increased from 400 to
1200Hz. Figure 2 shows the bunch shape at injection and at 150msec after
injection. The signals, plotted here with 5nsec/div, were obtained with
a wall current monitor. It is clear that the frequency separation of
1200Hz is enough to keep the bunch shape unchanged.

![](media/image2.jpeg){width="5.997916666666667in"
height="4.582638888888889in"}

Figure 2. Wall current monitor signals at injection and after 0.15msec.

**4. RF system**

MI has 18 53MHz cavities. These are in to two groups, A and B, each with
9 cavities. Low level RF (LLRF) signals go to two groups of cavities
individually. For the slip stacking, we are using one out of 9 cavities
in each group at injection. The rf voltage at injection is adjusted so
that one cavity produces 62 kV in order to achieve a low momentum
spread.

**5. Injection matching from Booster to MI**

At extraction, the Booster rf voltage is 380kV, which matches to MI
injection voltage of 1MV for the normal operation. Since the MI
injection rf voltage is 62 kV for the slip stacking, a bunch rotation is
carried out in Booster before extraction so that the bunch shape will be
matched to the rf bucket of MI at injection. As the Booster rf voltage
is rapidly reduced, the bunch starts to rotate in the phase space. After
a quarter of synchrotron period, the bunch is injected to MI. Figure 4
shows the wall current monitor (WCM) signal at Booster extraction. The
rf voltage was changed from 380kV to 130kV in 50μsec and the bunch
started a rotation with the rotation period of \~300μsec.

![](media/image3.jpeg){width="6.0in" height="4.5in"}

Figure 3. Bunch rotation process at Booster extraction. WCM voltage as a
function of time.Horizontal scale is 100μsec/div.

**6. RF frequency curves**

The frequency as a function of time is shown in Figure 4 for the first
and the second rf systems. Of 18 cavities at 53MHz, one was used for the
first system, another for the second system. The frequency separation
was kept at 1200Hz. The first bunch train was injected on the central
orbit with nominal frequency at 0.13msec and captured by the first rf
system of 62kV. At this time, the frequency of the second rf system was
1200Hz higher than the first rf system. The first bunch was then
decelerated to the frequency 1200Hz lower than the original value. After
one Booster cycle of 66.7msec, the second train was injected on the
central orbit and captured by the second rf system. After slipping, both
bunch trains were captured by all 18 cavities with 800kV and 0 frequency
separation.

![](media/image4.jpeg){width="6.0in" height="4.5in"}

Figure 4. Frequency for 1^st^ bunch train and 2^nd^ bunch train as a
function of time.

**7. Beam studies with low intensity for slip stacking**

Two bunch trains, each with 82 bunches, were injected to MI. The total
intensity for two trains was low, 0.8\*10^12^ppp, in order to reduce
beam loading effects.

Figure 5, a mountain range picture of the signals from the WCM, reveals
the progress of slip stacking from the beginning to the end. The signal
came from WCM with a resolution of 0.5nsec/sample. The data were
obtained every 1.42msec for 0.18sec. At the same time, the total
beam-intensity and the intensity within the gate equivalent to one rf
bucket width were also measured and plotted in Fig.6. The one bucket
intensity was 9E9 which is equal to 0.8E12/(82\*2). This indicates that
there was no beam loss during the slip stacking process. The intensity
of the 1^st^ bunch of the1^st^ bunch train was estimated by integration
of bunch area obtained by the WCM. Figure 7 shows the result of the
integration and the position of the center of the bunch. When two
bunches were recaptured by one rf bucket after 0.17 sec, the intensity
became twice of what was before while the bunch position did not move.

The length of the 1^st^ bunch of the 1^st^ bunch train shown in Fig. 5
was used to estimate the emittance. Figure 8 shows the estimated 95%
emittance during 0.18sec. Since there was an empty space between upper
and lower bunches, there should be an emittance growth. The calculated
growth rate is a factor of 3.2. From the plot, we see that there is no
emittance growth before the two batches are recaptured by one rf bucket
but there is a factor of 4.0 emittance growth after the recapture.

![](media/image5.jpeg){width="5.25in" height="3.9375in"}

Figure 5. Mt range plot. The signal came from WCM with a resolution of
0.5nsec/sample. The data were obtained every 1.42msec for 0.18sec.

![](media/image6.jpeg){width="4.879861111111111in"
height="3.667361111111111in"}

Figure 6. Total beam-intensity(I:BEAMM) and the intensity within the
gate equivalent to one RF bucket width at 2000nsec(I:P1ING),
2400nsec(I:P2ING) and 2800nsec(I:P3ING).

![](media/image7.jpeg){width="5.5in" height="4.125in"}

Figure 7. The intensity of the 1^st^ bunch of the1^st^ bunch train was
estimated by integration of bunch area shown in Fig.5. The center
position of the bunch was also measured.

![](media/image8.jpeg){width="5.5in" height="4.125in"}

Figure 8. The 95% emittance estimated by bunch length shown in Fig.5.

**8. Simulation studies**

To understand what caused the emittance growth at recapture, simulation
studies were carried out using the code, ESME. In the simulation
studies, the time and voltage to recapture bunches were varied because
LLRF timing had a jitter and also the rf voltage was changing after the
recapture as shown in Fig. 9.

Figure 10 shows the phase space at recapture time. The delay was changed
from 0 to 250 μsec and the 95 % bunch length after 15msec was measured.
The emittance plotted in Fig. 11 was estimated from the bunch length. It
is increased by a factor of 3.2 to 7.0 with increasing delay. Since LLRF
has a time jitter of 1.38msec maximum, it could cause the emittance
growth.

The recapture voltage was changed from 0.5 to 1.0MV because the voltage
is changing from 0.8 to 1.0MV after the time to recapture. The 95%
emittance plotted in Fig. 12 shows the emittance growth by a factor of
3.2 to 3.6.

By the two simulation studies, it was verified that the emittance growth
is mainly due to LLRF jitter.

![](media/image9.png){width="6.0in" height="4.5in"}

Figure 9. Total rf voltage(I:RFSUML).

![](media/image10.jpeg){width="6.0in" height="8.0in"}

Figure 10. The phase space at recapture time and bunch shape after
15msec. The delay were 0sec(upper), 100μsec(middle) and 250 μsec(lower).

![](media/image11.jpeg){width="5.75in" height="4.319444444444445in"}

Figure 11. The 95% emittance estimated VS recapture delay time.

![](media/image12.jpeg){width="5.75in" height="4.3125in"}

Figure 12. The 95% emittance estimated VS recapture rf voltage.

# 9. Conclusion

Beam studies have stared for the slip stacking process and we have
already verified that, at least for low beam intensity, the stacking
procedure works as expected.

There was no beam loss during the process, but there was emittance
growth when two bunch trains were recaptured. Simulation studies have
indicated that the emittance growth is caused by LLRF timing jitter.
During a shutdown (Jan.13 03 \~ Feb.03 03), the LLRF jitter was improved
to the resolution of 10 μsec and this should help reducing the emittance
growth.

For higher intensity operation, development work of the feedback and
feedforward system is under way.