# Preliminary Design of a 1.3 GHz β = 0.81 

# Multi-cell Elliptical Cavity

## September 29, 2005

> C. Compton, T. Grimm, W. Hartung, M. Johnson, D. Meidlinger, R.C. York
>
> Michigan State University
>
> B. Foster, N. Solyak, V. Yarba
>
> Fermi National Accelerator Laboratory
>
> P. Kneisel
>
> Thomas Jefferson National Laboratory

## 

## Abstract

> The preliminary design of a 1.3 GHz, β=v/c=0.81, seven cell elliptical
> cavity for FNAL's proton driver is presented. The first stage of
> prototyping will consist of single-cell cavities made from two types
> of high purity niobium (fine grain and large grain). The end cell
> design will be used for the single-cell prototypes, since its beam
> tubes match those of TESLA.

## Outline

> Design Criteria
>
> 7-Cell Design -- Symmetric Design
>
> Mid Cell Geometry
>
> End Cell Geometry
>
> Comparison to TESLA & SNS
>
> Single Cell Prototype -- end cell
>
> Fine & Large grain
>
> Flange Design
>
> Vertical test configuration at MSU

## Design Criteria

> It was determined that the proton driver
> $\beta = 0\text{.}\text{81}$cavity shall meet the following criteria:

1.  Maintain $\frac{B_{p}}{E_{p}}$ similar to TESLA or
    $\frac{\text{110}\text{mT}}{\text{51}\text{.}6\frac{\text{MV}}{m}} = 2\text{.}\text{13}\frac{\frac{\text{mT}}{\text{MV}}}{m}$.

2.  Cell-to-cell coupling of 1.6% that is consistent with adequate field
    flatness in a seven-cell structure.

3.  A wall angle similar to SNS of about 7º to reduce risk of incomplete
    cleaning.

4.  Beam tubes same diameter as TESLA cavities.

5.  Flanges based on 4-5/8 inch Nb45-Ti Conflat® geometry.

## 7-Cell Cavity Design -- Symmetric Design

> The SNS shape meets these criteria with the exception of a reduced
> cell-to-cell coupling of 1.5%. The proton driver mid cell is therefore
> similar to the SNS shape but has a larger aperture radius resulting in
> a cell-to-cell coupling of 1.60%. The equatorial and iris ellipse
> shapes necessarily changed to conform with items 1 and 3 above. The
> geometry of the mid cells are given in Table 1. The figures of merit
> for the proton driver mid cells are shown in Table 2. The mid cell
> shape is shown in Figure 1. The peak field ratios of the mid cell are
> very close to the original SNS ratios of
> $\frac{E_{p}}{E_{a}} = 2\text{.}\text{14}$ and
> $\frac{B_{p}}{E_{a}} = 4\text{.}\text{58}\frac{\frac{\text{mT}}{\text{MV}}}{m}$.
>
> *Table 1. Geometry for the proton driver mid-cells.*

+------------------+------------------------+-------------------------+
| #### B           | > cm                   | > 4.371                 |
+------------------+------------------------+-------------------------+
| > A              | > cm                   | > 3.362                 |
+------------------+------------------------+-------------------------+
| > a              | > cm                   | > 1.138                 |
+------------------+------------------------+-------------------------+
| > b              | > cm                   | > 2.088                 |
+------------------+------------------------+-------------------------+
| > D              | > cm                   | > 10.3131               |
+------------------+------------------------+-------------------------+
| > $$R            | > cm                   | > 3.05                  |
| _{\text{iris}}$$ |                        |                         |
+------------------+------------------------+-------------------------+
| > d              | > cm                   | > 0.91                  |
+------------------+------------------------+-------------------------+
| > α              | > degrees              | > 7                     |
+------------------+------------------------+-------------------------+
| > L              | > cm                   | > 4.67                  |
+------------------+------------------------+-------------------------+

> Table 2. Figures of merit for the proton driver mid-cells.

+--------------------------+-------------------------+-----------------+
| >                        | > \-                    | > 2.15          |
|  $$\frac{E_{p}}{E_{a}}$$ |                         |                 |
+--------------------------+-------------------------+-----------------+
| >                        | > *mT/MV/m*             | > 4.58          |
|  $$\frac{B_{p}}{E_{a}}$$ |                         |                 |
+--------------------------+-------------------------+-----------------+
| > Frequency              | > MHz                   | > 1300          |
+--------------------------+-------------------------+-----------------+
| > $$\frac{R}{Q}$$        | > Ω                     | > 82.0          |
+--------------------------+-------------------------+-----------------+
| > G                      | > Ω                     | > 226           |
+--------------------------+-------------------------+-----------------+
| > $$k_{\text{cc}}$$      | > \%                    | > 1.60          |
+--------------------------+-------------------------+-----------------+

> For this initial design, the proton driver end cells are the same
> resulting in a symmetrical cavity. Table 3 lists the end cell geometry
> using the parameters shown in Figure 1. The right half of the *7*-cell
> cavity is shown in Figure 2. The field values on the surface of the
> cavity are displayed in Figure 3. The distance is measured starting
> from an initial point at the equator of the middle cell then moving
> along the outer cavity surface toward the beam pipe. The peak magnetic
> field for each cell is approximately equal and the peak electric field
> occurs at the iris of a mid cell. The on-axis axial electric field is
> displayed in Figure 4 showing a field unflatness of *0.9%.* The cavity
> figures of merit are listed in Table 4 where the SNS and TESLA values
> are also given for purposes of comparison. In conforming to criteria
> number 4, the proton driver will use the same beam tubes as the TESLA
> design (radius =3.90 cm) in contrast to the SNS design which uses two
> different beam tubes (radii of 3.022 cm and 4.335 cm).
>
> ![](media/image1.png){width="1.8458333333333334in"
> height="3.365972222222222in"}![](media/image2.png){width="2.8222222222222224in"
> height="3.529166666666667in"}
>
> Figure 1. π-mode electric field lines of a mid-cell for the case of an
> infinitely long structure.
>
> ![](media/image3.wmf){width="6.750694444444444in"
> height="1.3458333333333334in"}
>
> Figure 2. Electric field lines for the π-mode of the 7-cell cavity.
>
> ![](media/image4.jpeg){width="6.496527777777778in"
> height="4.605555555555555in"}
>
> Figure 3. Surface fields on 3.5 cells of the 7-cell cavity
>
> ![](media/image5.jpeg){width="6.490972222222222in"
> height="3.7840277777777778in"}
>
> Figure 4. Axial electric field profile with field un-flatness = 0.9%.
>
> Table 3. Geometry for the proton driver end cell.

+------------------+------------------------+-------------------------+
| > B              | > Cm                   | > 3.167                 |
+------------------+------------------------+-------------------------+
| > A              | > Cm                   | > 3.167                 |
+------------------+------------------------+-------------------------+
| > a              | > cm                   | > 1.338                 |
+------------------+------------------------+-------------------------+
| > b              | > cm                   | > 2.341                 |
+------------------+------------------------+-------------------------+
| > D              | > cm                   | > 10.3131               |
+------------------+------------------------+-------------------------+
| > $$R            | > cm                   | > 3.9                   |
| _{\text{iris}}$$ |                        |                         |
+------------------+------------------------+-------------------------+
| > d              | > cm                   | > 1.081                 |
+------------------+------------------------+-------------------------+
| > α              | > degrees              | > 7                     |
+------------------+------------------------+-------------------------+
| > L              | > cm                   | > 4.67                  |
+------------------+------------------------+-------------------------+

### Comparison to TESLA & SNS

The preliminary design of a 7-cell, β = 0.81 elliptical cavity should
have good field flatness while achieving the present design criteria.
Two primary differences from the SNS design are the increased
cell-to-cell coupling and the use of TESLA beam tubes. As a next step,
multipacting simulations will be done, and a second end cell design may
be considered to improve higher order mode suppression.

> Table 4. Parameters of 1300 MHz cavities, assuming
> $B_{p} = \text{110}\text{mT}$

+-------------+-------------+----------+--------------+---------------+
|             |             | > TESLA  | > Scaled SNS | > Proton      |
|             |             |          |              | > Driver      |
+-------------+-------------+----------+--------------+---------------+
| > Β         | > \-        | > 1      | > 0.81       | > 0.81        |
+-------------+-------------+----------+--------------+---------------+
| > Wall      | > degrees   | > 13.3   | > 7          | > 7           |
| > angle     |             |          |              |               |
+-------------+-------------+----------+--------------+---------------+
| > $         | > \-        | > 2.0    | > 2.19       | > 2.19        |
| $\frac{E_{p |             |          |              |               |
| }}{E_{a}}$$ |             |          |              |               |
+-------------+-------------+----------+--------------+---------------+
| > $         | > mT/MV/m   | > 4.26   | > 4.79       | > 4.71        |
| $\frac{B_{p |             |          |              |               |
| }}{E_{p}}$$ |             |          |              |               |
+-------------+-------------+----------+--------------+---------------+
| > $$k_{\    | > \%        | > 1.8    | > 1.5        | > 1.6         |
| text{cc}}$$ |             |          |              |               |
+-------------+-------------+----------+--------------+---------------+
| > $$\frac   | > Ω         | > 115    | > 80.8       | > 79.1        |
| {R}{Q}\text |             |          |              |               |
| {percell}$$ |             |          |              |               |
+-------------+-------------+----------+--------------+---------------+
| > G         | > Ω         | > 270    | > 233        | > 227         |
+-------------+-------------+----------+--------------+---------------+
| > $$B_{p}$$ | > mT        | > 110    | > 110        | > 110         |
+-------------+-------------+----------+--------------+---------------+
| > $$E_{a}$$ | > MV/m      | > 25.8   | > 23.0       | > 23.4        |
+-------------+-------------+----------+--------------+---------------+
| > $$E_{p}$$ | > MV/m      | > 51.6   | > 50.4       | > 51.1        |
+-------------+-------------+----------+--------------+---------------+

## Single Cell Prototype

### Fine & large grain

A total of six single cell cavities will be manufactured from high RRR,
2.8 mm thick sheet. Three cavities will be constructed from fine grain
niobium, and three from large grain niobium that was EDM wire cut. This
will allow the effect of material composition to be evaluated with some
modest statistics.

### Single Cell Cavity Design -- end cell

> A section of single cell cavity design, developed from the end cell
> parameters in Table 3, is shown in Figures 5 and 6. The
> electromagnetic parameters are in Table 5. The design uses extruded
> niobium tubes purchased from industry with 4-5/8" Conflat® Nb45-Ti end
> flanges. The half-cells will be deep drawn using 7075-T6 aluminum dies
> machined at MSU and all electron beam welding will be done at Sciaky
> Corp.
>
> ![](media/image6.wmf){width="6.6125in" height="5.158333333333333in"}
>
> Figure 5. Cavity detail drawing of the single cell prototype.

### ![](media/image7.png){width="6.485416666666667in" height="2.90625in"}

> Figure 6. Electric field lines of the single-cell prototype.
>
> Table 5. Parameters of the single-cell prototype, assuming
> $B_{p} = \text{110}\text{mT}$ and β = 0.81.

+----------------------+----------------------+-----------------------+
|                      |                      | > Single Cell         |
+----------------------+----------------------+-----------------------+
| > Wall angle         | > degrees            | > 7                   |
+----------------------+----------------------+-----------------------+
| > $$\                | > \-                 | > 2.18                |
| frac{E_{p}}{E_{a}}$$ |                      |                       |
+----------------------+----------------------+-----------------------+
| > $$\                | > mT/MV/m            | > 5.26                |
| frac{B_{p}}{E_{p}}$$ |                      |                       |
+----------------------+----------------------+-----------------------+
| > $$\frac{R}{Q}$$    | > Ω                  | > 62.3                |
+----------------------+----------------------+-----------------------+
| > G                  | > Ω                  | > 229                 |
+----------------------+----------------------+-----------------------+
| > $$B_{p}$$          | > mT                 | > 110                 |
+----------------------+----------------------+-----------------------+
| > $$E_{a}$$          | > MV/m               | > 20.9                |
+----------------------+----------------------+-----------------------+
| > $$E_{p}$$          | > MV/m               | > 45.6                |
+----------------------+----------------------+-----------------------+

### Flange Design

> The cavity's end flange design will be made utilizing Nb45-Ti 4-5/8"
> standard Conflat® compatible geometry. The advantages of using a
> standard commercial Conflat® connection include simplified vacuum
> components during the testing phase and readily available copper
> gaskets that can be purchased from multiple vendors.

In the case that a seal cannot be made with the standard Conflat® method
or if there is a later requirement to use an alternate seal, the Nb45-Ti
flange can be modified to use aluminum or indium sealing methods. The
process of adapting the Conflat® flange to the alternate sealing method
is to machine away the standard knife-edge and face off the flange to a
counter bore with the appropriate surface finish allowing an aluminum or
indium seal. The flange in both configurations is shown in Figure 7.

> ![](media/image8.wmf){width="2.857638888888889in"
> height="2.058333333333333in"}
> ![](media/image9.wmf){width="2.7465277777777777in"
> height="2.222916666666667in"}
>
> Figure 7. Cavity flange design using commercial Conflat® (A) and
> alternate sealing method that machines away knife-edge to use an
> aluminum diamond shaped gasket (B).

### 

### Vertical Test Configuration at MSU

Testing done at MSU will be performed in the \~200 L vertical testing
dewar. The single cell cavity-testing layout is shown in Figure 8.
During cool down from room temperature to 2K transition pressures can
reach 2 bar externally on the cavity; a holding fixture has been
included to prevent any permanent deformation to the cavity from these
pressures. The 2K helium camera viewing system will also be used during
testing of the cavities to observe any helium gas formation showing
sites of localized heating. The RF power and pickup feedthrus will be
standard type-N connections.

> ![](media/image10.png){width="3.1in"
> height="2.8354166666666667in"}![](media/image11.jpeg){width="2.9291666666666667in"
> height="2.678472222222222in"}

Figure 8. Single cell vertical testing in MSU's \~200 liter helium dewar
(A). Closer view of RF feedthrus, holding fixture and single cell cavity
(B).