LARP IR Cryogenics: Sector 4-5 Heat Load Study for the 10^35^/cm^2^-s
LHC Luminosity Upgrade

Roger Rabehl

July 25, 2006

# Introduction

The goal of the LHC Accelerator Research Program (LARP) is to contribute
to the LHC luminosity upgrade from 10^34^/cm^2^-s to 10^35^/cm^2^-s.
This upgrade will likely occur in a number of phases \[1\]. One
contribution LARP is focusing on is the interaction region (IR)
upgrades. The increased heat loads resulting from the luminosity upgrade
will affect not only the thermal design of the IR's, but also the LHC
cryogenics system as a whole. This document attempts to address this
question by scaling the cryogenics system heat loads and determining the
significance of the IR heat loads relative to the system heat loads.

Sector 4-5 (a high-load sector) is analyzed in this document. Only the
heat loads to 1.9 K and 4.6-20 K are considered because they are the
temperature levels most relevant to the inner triplet.

**Analysis**

[LHC Luminosity Upgrade Options]{.underline}

Two of the LHC luminosity upgrades being considered are the short bunch
and long bunch options. The short bunch option has twice as many total
particles as ultimate luminosity with twice as many bunches but half the
bunch length. The long bunch option has about 15% more total particles
than ultimate luminosity but only one-third the number of bunches and a
bunch length twice as long. The parameters listed in Table 1 are
relevant for estimating the system heat load for the two luminosity
upgrade scenarios.

**[Table 1]{.underline}** Parameters for LHC upgrade options \[2, except
for the next to last row\].

  -------------------- ------------ ------------ ----------------- -----------------
  Parameter            Nominal      Ultimate     Short bunch       Long bunch
                       luminosity   luminosity   luminosity        luminosity
                                                 upgrade           upgrade

  Beam current,        0.58         0.86         1.72              1.0
  I~beam~ \[A\]                                                    

  No. of bunches,      2808         2808         5616              936
  n~bunch~                                                         

  Bunch length         7.55         7.55         3.78              14.4
  (r.m.s.), ~z~ \[cm\]                                             

  Luminosity, L        1.0          2.3          9.2               8.9
  \[10^34^/cm^2^-s\]                                               

  Bunch current,       0.21         0.31         0.31              1.07
  I~bunch~ \[mA\]                                                  

  Long. Profile        Gaussian     Gaussian     Gaussian          Flat
  -------------------- ------------ ------------ ----------------- -----------------

The bunch current, or bunch intensity, is calculated by Equation 1.

$I_{\text{bunch}} = \frac{I_{\text{beam}}}{n_{\text{bunch}}}$ (1)

[Heat Load Scaling]{.underline}

The scaling laws of Table 2 can be used to estimate cryogenic system
heat loads for each of the luminosity upgrade scenarios based on the
parameters in Table 1. For the upgrade scenarios considered here, the
relevant parameters are bunch current I~bunch~, number of bunches
n~bunch~, bunch length ~z~, and luminosity L.

**[Table 2]{.underline}** Scaling laws of beam-induced loads \[3\].

+----------------+------+-----------+-----------+----------+---------+
| Beam parameter | En   | Bunch     | Bunch     | Bunch    | Lum     |
|                | ergy | current   | number    | length   | inosity |
|                |      |           |           |          |         |
|                | E    | I~bunch~  | n~bunch~  | ~z~      | L       |
|                |      |           |           | \[       |         |
|                |      |           |           | r.m.s.\] |         |
+----------------+------+-----------+-----------+----------+---------+
| Resistive      | E^2^ | \-        | \-        | \-       | \-      |
| heating        |      |           |           |          |         |
+----------------+------+-----------+-----------+----------+---------+
| Synchrotron    | E^4^ | I~bunch~  | n~bunch~  | \-       | \-      |
| radiation      |      |           |           |          |         |
+----------------+------+-----------+-----------+----------+---------+
| Image current  | \-   | I~        | n~bunch~  | ~        | \-      |
|                |      | bunch~^2^ |           | z~^-3/2^ |         |
+----------------+------+-----------+-----------+----------+---------+
| Photo-electron | \-   | I~        | n~bunch~  | \-       | \-      |
| cloud          |      | bunch~^3^ |           |          |         |
+----------------+------+-----------+-----------+----------+---------+
| Beam gas       | \-   | I~bunch~  | n~bunch~  | \-       | \-      |
| scattering     |      |           |           |          |         |
+----------------+------+-----------+-----------+----------+---------+
| Random         | \-   | I~bunch~  | n~bunch~  | \-       | \-      |
| particle loss  |      |           |           |          |         |
+----------------+------+-----------+-----------+----------+---------+
| Secondaries    | E    | \-        | \-        | \-       | L       |
+----------------+------+-----------+-----------+----------+---------+
| RF losses      | \-   | I~        | n~bunch~  | \-       | \-      |
|                |      | bunch~^2^ |           |          |         |
+----------------+------+-----------+-----------+----------+---------+

At nominal luminosity, the latest photo-electron cloud numbers are
reduced by 2/3 from those in the LHC Design Report. At ultimate
luminosity, these numbers are reduced by slightly more than 2/3. The
electron cloud heat load varies with bunch intensity by a third-power
law but there is often a weaker dependence, especially at higher bunch
intensities. Also, a decrease in heat load becomes noticeable from about
twice the nominal bunch length. Long, flat bunches or super-bunches
generate less heat load per proton than at the nominal LHC conditions
\[4\]. Therefore, the photo-electron heat load for the long bunch
upgrade is assumed to be equal to that at ultimate luminosity due to the
high bunch intensity and the long, flat bunch profile.

**[Table 3]{.underline}** Distributed steady-state beam-induced loads in
an LHC cell \[mW/m\]

\[5; 6 (photo-electron cloud numbers)\]

  ------------------ ------------ ------------ ------------- -------------
                     Nominal                   Ultimate      
                     luminosity                luminosity    

  Temperature        4.6-20 K     1.9 K        4.6-20 K      1.9 K

  Synchrotron        330          1            500           1
  radiation                                                  

  Image current      360          1            820           2

  Photo-electron     600          6            900           9
  cloud                                                      

  Beam-gas           0.4          48           0.4           48
  scattering                                                 

  Random particle    0-0.1        0-32         0-0.3         0-48
  loss                                                       

  Total beam-induced 1290         56-88        2220          60-108

                                                             

                     Short bunch               Long bunch    
                     upgrade                   upgrade       

  Temperature        4.6-20 K     1.9 K        4.6-20 K      1.9 K

  Synchrotron        1000         2            575           1
  radiation                                                  

  Image current      4629         11           1236          3

  Photo-electron     1800         18           900           9
  cloud                                                      

  Beam-gas           0.8          96           0.5           55
  scattering                                                 

  Random particle    0-0.6        0-96         0-0.3         0-55
  loss                                                       

  Total beam-induced 7430         127-223      2712          68-123
  ------------------ ------------ ------------ ------------- -------------

[Sector Heat Load Calculations]{.underline}

The heat load estimates of Table 3 can be applied to estimate the heat
load for a given sector of the LHC. This document presents calculated
results for sector 4-5, a high-load sector. Table A-1 in the Appendix
summarizes the sector 4-5 heat load calculations for nominal luminosity,
ultimate luminosity, short bunch upgrade, and long bunch upgrade
operation, respectively. The calculations are detailed in Tables A-2
through A-5 of the Appendix.

With the exception of the photo-electron heat loads, the nominal and
ultimate heat loads are taken from the LHC Design Report as indicated.
Heat loads for the short bunch and long bunch upgrades are then
calculated using the scaling laws of Table 2. The dispersion suppressor
heat loads are assumed to scale similarly to the arc heat loads. The
4.6-20 K inner triplet heat load is assumed to be dominated by the
photo-electron effect and is scaled accordingly. The 1.9 K inner triplet
heat load is assumed to be dominated by the secondary particles as
calculated by N. Mokhov (FNAL).

**[Table 4]{.underline}** Installed refrigeration capacity in the LHC
sectors \[7\].

  ----------------------------------- ----------------- -----------------
  Temperature level                   High-load sector  Low-load sector

  50-75 K \[W\]                       33000             31000

  4.6-20 K \[W\]                      7700              7600

  4.5 K \[W\]                         300               150

  1.9 K LHe \[W\]                     2400              2100

  4 K VLP \[W\]                       430               380

  20-280 K \[g/s\]                    41                27
  ----------------------------------- ----------------- -----------------

Figure 1 summarizes the calculated 4.6-20 K heat loads. Based on current
estimates, the installed refrigeration capacity is slightly below the
ultimate luminosity heat load. Both the short and long bunch upgrades
would require system upgrades, with the short bunch upgrade requiring a
significantly more extensive upgrade due to the photo-electron effect.

![](media/image1.wmf){width="5.998611111111111in" height="3.19375in"}

**[Figure 1]{.underline}** Calculated 4.6-20 K heat loads for sector 4-5
at nominal, ultimate, short bunch upgrade, and long bunch upgrade
luminosities.

Similarly, Figure 2 shows the calculated 1.9 K heat loads. The installed
capacity is estimated to be sufficient for nominal and ultimate
luminosity operations. The installed capacity is exceeded by the heat
loads of both the short bunch and long bunch upgrades. The inner triplet
dynamic heat load to 1.9 K is indicated for each luminosity, and for
both upgrade scenarios it is a significant fraction of the total sector
heat load.

![](media/image2.wmf){width="5.992361111111111in"
height="3.2090277777777776in"}

**[Figure 2]{.underline}** Calculated 1.9 K heat loads for sector 4-5 at
nominal, ultimate, short bunch upgrade, and long bunch upgrade
luminosities.

**Conclusions**

Both luminosity upgrade scenarios will require cryogenic upgrades to the
4.6-20 K system. A much more extensive cryogenic upgrade will be
required if the short bunch luminosity upgrade is chosen.

The installed 1.9 K capacity is not sufficient for either luminosity
upgrade scenario. The inner triplet heat load is significant for both
luminosity upgrade scenarios.

A number of possible cryogenic system upgrades can be envisioned and
have been discussed elsewhere \[8\]. Among the possibilities are:

-   Upgrade the 4.6-20 K and 1.9 K systems to meet the heat loads of
    Figure 1 and 2.

-   Intercept a sizable fraction of the inner triplet 1.9 K heat load at
    a higher temperature (e.g., using 4.6-20 K absorbers). This would
    minimize or even eliminate a 1.9 K capacity upgrade while requiring
    a larger 4.6-20 K capacity upgrade.

-   Upgrade the 4.6-20 K system to meet the heat loads of Figure 1 while
    adding 1.9 K plants dedicated to cooling the inner triplets.

#### References

\[1\] F. Ruggiero, "LHC Upgrade Scenarios and Interaction Region
Design," LHC IR Upgrades Workshop, St. Charles, IL, October 3-4, 2005.

\[2\] Ibid

\[3\] LHC Design Report Volume 1, Chap. 8, Table 11.7, p. 316.

(<http://ab-div.web.cern.ch/ab-div/Publications/LHC-DesignReport.html>)

\[4\] F. Zimmerman, private communication, February 2006.

\[5\] LHC Design Report Volume 1, Chap. 8, Table 11.8, p. 316.

> (<http://ab-div.web.cern.ch/ab-div/Publications/LHC-DesignReport.html>)

\[6\] F. Zimmerman, "LHC electron-cloud update," p.10, LHC MAC 10, June
2005.

> (<http://mgt-lhc-machine-advisory-committee.web.cern.ch/mgt-lhc-machine-advisory-committee/lhcmac17/ClosedSession/Zimmermann.pdf>)

\[7\] LHC Design Report Volume 1, Chap. 8, Table 11.11, p. 328.

> (<http://ab-div.web.cern.ch/ab-div/Publications/LHC-DesignReport.html>)

\[8\] F. Ruggiero, et al., "LHC Luminosity and Energy Upgrade: A
Feasibility Study," LHC Project Report 626, December 2002.

**Appendix**

**[Table A-1]{.underline}** Sector 4-5 heat load summary.

![](media/image3.png){width="4.892361111111111in"
height="8.03888888888889in"}

**[Table A-2]{.underline}** Nominal luminosity sector 4-5 heat load
summary.

![](media/image4.png){width="5.992361111111111in"
height="8.078472222222222in"}

**[Table A-3]{.underline}** Ultimate luminosity sector 4-5 heat load
summary.

![](media/image5.png){width="5.992361111111111in"
height="8.078472222222222in"}

**[Table A-4]{.underline}** Short bunch luminosity upgrade sector 4-5
heat load summary.

![](media/image6.png){width="5.992361111111111in"
height="8.078472222222222in"}

**[Table A-5]{.underline}** Long bunch luminosity upgrade sector 4-5
heat load summary.

![](media/image7.png){width="5.992361111111111in"
height="8.078472222222222in"}