# HIGH LEVEL RF FOR THE SNS RING\*

A. Zaltsman, M. Blaskiewicz, J. Brennan, J. Brodowski, M. Meth, R.
Spitz, F. Severino,

BNL, New York 11973, USA

#### **1. ABSTRACT**

A high level RF system (HLRF) consisting of power amplifiers (PA\'s) and
ferrite loaded cavities is being designed and built by Brookhaven
National Laboratory (BNL) for the Spallation Neutron Source (SNS)
project. It is a fixed frequency, two harmonic system whose main
function is to maintain a gap for the kicker rise time. Three cavities
running at the fundamental harmonic (h=1) will provide 40 kV and one
cavity at the second harmonic (h=2) will provide 20 kV. Each cavity has
two gaps with a design voltage of 10 kV per gap and will be driven by a
power amplifier (PA) directly adjacent to it. The PA uses a 600kW
tetrode to provide the necessary drive current. The anode of the tetrode
is magnetically coupled to the downstream cell of the cavity. Drive to
the PA will be provided by a wide band, solid state amplifier located
remotely. A dynamic tuning scheme will be implemented to help compensate
for the effect of beam loading.

**2. INTRODUCTION**

Main tasks of the HLRF system for the SNS ring is to capture proton beam
during 1 ms injection from the 1GeV linac and to maintain a gap for the
rise time of the extraction kicker. The HLRF system consists of three
harmonic one cavities running at 1.05 MHz and one harmonic two cavity at
2.1 MHz.

The HLRF will be required to operate at wide dynamic ranges of the gap
voltage (20 dB) and from no beam loading at the beginning of the cycle
to the heavy beam loading (75 Amps peak current) at the end.

This paper will describe all the key components of the HLRF system with
the emphasis on the ways to cope with the heavy beam loading.

## 3. sYSTEM PARAMETERS

High beam loading and reliability of the system are determining factors
for the system configuration and parameters. Table 1 is a tabulation of
the RF parameters:

To achieve these requirements, a set of parameters was developed. These
parameters take into consideration beam loading, reliable high voltage
design, availability of components (ferrites, tubes, etc.), space in the
ring and maintainability.

\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

\*Work performed under the auspices of the United States Department of
Energy

**Table I**

+----------------------------------------+-----------------------------+
| *Parameter*                            | ##### Value                 |
+----------------------------------------+-----------------------------+
| Circumference                          | 248 m                       |
+----------------------------------------+-----------------------------+
| Total h=1 voltage                      | 40 kV                       |
+----------------------------------------+-----------------------------+
| Total h=2 voltage                      | 20 kV                       |
+----------------------------------------+-----------------------------+
| Space charge Z/n                       | i200 Ω                      |
+----------------------------------------+-----------------------------+
| Proton kinetic energy                  | 1Gev                        |
+----------------------------------------+-----------------------------+
| Injection bunch length                 | 610 ns                      |
+----------------------------------------+-----------------------------+
| Injection energy spread                | +/- 3.8 MeV, full           |
+----------------------------------------+-----------------------------+
| Protons at extraction time             | 2.08 x 10^14^               |
+----------------------------------------+-----------------------------+
| Maximum bunch length                   | 650 ns                      |
+----------------------------------------+-----------------------------+
| Peak beam current                      | 75 Amps                     |
+----------------------------------------+-----------------------------+

System parameters are tabulated in Table II.

**Table II**

  ---------------------------------------- ------------------------------
  RF system type                           Dual harmonic

  Cavity length                            2.3 m

  Accelerating gaps per cavity             2

  Harmonic 1 frequency                     1.058 MHz

  Number of harmonic 1 cavities            3

  Harmonic 1 total voltage                 40 kV

  Harmonic 2 frequency                     2.115 MHz

  Number of harmonic 2 cavities            1

  Harmonic 2 total voltage                 20 kV

  Beam loading compensation                Dynamic tuning and feed
                                           forward

  Harmonic 1 cavity shunt impedance        800 Ω
  ---------------------------------------- ------------------------------

##  4. Cavity AND POWER AMPLIFIER

Reliability, conservative design and easy maintainability were the prime
consideration in the development of the SNS RF system. From past
experience in the AGS and AGS Booster, we learned that the most
optimized and conservative voltage across the gap is 10 kV. To keep the
gap voltage at or below 10 kV, and keep flux density as well as power
dissipation at reasonable levels, a two gap RF cavity was designed. In
this design, two gaps are single ended and ferrite loaded. Gaps are
interconnected by buswork, which, for symmetry, and to reduce
inductance, are in front and in the rear of the cavity.

Small samples, as well as full size ferrite rings, were evaluated for
power dissipation, permeability and instabilities. The best choice for
the ferrite for this application was Philips 4M2. The highest flux
density is at the lowest frequency and on the inner surface of the
ferrite ring. Each gap consists of 21 rings, and each ring measured 50cm
O.D x 25cm I.D. x 2.72cm thick.

$$V\text{gap} = 2 \cdot \pi \cdot f \cdot B\text{rf} \cdot l \cdot a \cdot \text{ln}(\frac{b}{a})$$

$$B\text{rf}\text{max} = \frac{\text{10}^{4}}{6\text{.}\text{28} \cdot 1\text{.}\text{05}\text{MHz} \cdot \text{21} \cdot \text{.}\text{0272} \cdot \text{.}\text{125} \cdot \text{ln}\frac{\text{50}}{\text{25}}} = \text{310}\text{Gauss}$$

Tests of the ferrite showed no instabilities at flux density in excess
of 400 Gauss.

The ferrite power dissipation is taken care of by water cooling. A
cooling coil was constructed from dual rectangular copper conductor
wound in a spiral shape. Double disk grinding of the coils on both sides
provided the flatness and finish necessary for efficient heat transfer
between ferrite rings and the cooling plates without the use of thermal
conductive grease.

To reduce the beam loading, the R/Q should have the lowest possible
value. One way to achieve this is to increase the gap capacitance. In
our design, four capacitors of 750 pF each provide a total gap
capacitance of 3 nF. Our calculations show that, for f~rf~ = 1.05 MHz
the required inductance is 7.7 uH. To attain it, the initial
permeability of 145 should be reduced to 90 by the dc bias current.
Because removing 3 capacitors from the h=1 cavity will convert it to h=2
cavity, we are able to utilize the same cavity for both systems.

![](media/image1.wmf)

Figure 1

Figure \# 1 shows a functional diagram of the RF cavity and the PA.
Ferrite rings are dc biased whereas the outer can, beam pipe and the gap
connecting buswork form a single turn bias winding. Because two halves
of the cavity are in series to the dc bias, but in parallel to the RF
drive, the RF will be cancelled (figure eight).

Cavity is excited by a single tube class AB1 power output stage. The
amplifier is magnetically coupled to the cavity. B^+^ link is inserted
along the beam pipe. This technique eliminates the need for a plate
choke.

The power tube is a tetrode (Thomson TH558) chosen for it's high plate
dissipation (500 kW) and relatively low plate resistance (2kΩ). This
type of tube and its smaller version has been used in the BNL AGS RF
system for almost 10 years and it have proven to be very reliable.

The feedback (grid to plate) capacitance of the TH558 is 7pF, and has to
be neutralized for stable operation. Because the cavity is single-ended,
it was impossible to use the gap pick-up as a source of the inverted
signal, required for neutralization. To circumvent this difficulty, an
input transformer with a center tap was used to provide both the
inversion and a 2:1 step-up for the drive signal. ( see figure 2)

![](media/image2.wmf)

Figure 2

**5. DYNAMIC TUNING**

The beam current in the accumulator ring is in quadrature with the
generator current. During the accumulation the average beam current
increases from 0 to 35 amperes. The peak amplitude of the first harmonic
component is 50 amperes per gap with total 100 amperes per cavity.

$$Ib = 2 \cdot \text{10}^{\text{14}}\text{ppp} = \text{35}\text{Adc} = \text{55}\text{Apk}$$

By optimizing the resonant frequency of the cavity, the PA current may
be reduced to the unloaded value.

Set the gap voltage to $V(t) = V\text{rf}\text{sin}(\omega t)$ and the
PA current to
$I\text{pa}(t) = \left( \frac{V\text{rf}}{R} \right)\text{sin}(\omega t)$.

The beam current is $IB = Ib\text{cos}(\omega t)$.

The total driving current is the sum of the beam and PA contribution and
is equal to the sum of the currents in the resistor, capacitor and
inductor of the cavity.

$$\frac{V\text{rf}}{R}\text{sin}(\omega t) - Ib\text{cos}(\omega t)$$

> $$= \frac{V\text{rf}\text{sin}(\omega t)}{R} + \left( \omega C - \frac{1}{\omega L} \right)V\text{rf}\text{cos}(\omega t)$$

so, $Ib = V\text{rf}\left( \frac{1}{\omega L} - \omega C \right)$

The inductance is varied according to:

$- \frac{\Delta L}{L} = \frac{(RQ) \cdot Ib}{V\text{rf} + (RQ) \cdot Ib}$
where $\left( RQ = \frac{1}{\omega C} \right)$

$$\frac{\Delta L}{L} = \text{.}\text{35} = \text{35}\text{\%}$$

$\frac{\Delta f}{f} = - \frac{1}{2}\left( \frac{\Delta L}{L} \right) = \text{17}\text{\%}$

At 1.05 MHz it would represent 170 kHz frequency difference between the
drive frequency and the resonant frequency of the cavity. The loaded Q
of the cavity is 50 at tube quiescent current of 5 amperes, and drops to
38 at 10 amperes.

To simulate this mistuned condition the frequency was swept from 1.05
MHz to 1.22 MHz, while keeping the cavity tuned at the 1.05 MHz by the
constant tuning current. AGC kept the voltage on the gap constant at 7
kV. (Figure 3)

![](media/image3.png)

Figure 3

To tune the ferrite at the rate of 150 kHz in 1 ms (450 amperes/ ms)
would require a rather sophisticated transistor bank with at least 10
kHz bandwidth.

Dynamic tuning is a feed forward correction, which is perfect for the
SNS application since the repetition rate of the machine is 60 Hz, and
the beam intensity doesn't change from cycle to cycle. Tuning current
will be changing at 60 Hz (or multiple of it) +/-450 amperes peak around
the dc component needed to tune the cavity without the beam loading.

It was first tried on the test (2 ferrite ring) cavity. In this test we
used two separate tuning supplies: one to provide the dc component to
tune cavity to the resonance frequency, and second to resonate with
external cap bank at 60 cycles. The results were great, and a full power
tuning supply was built to test the final cavity.

![](media/image4.png)

Figure 4

Fig. 4 shows a dynamically tuned cavity: 10 kV on the gap with the tube
current less then 30 amperes. As you can see the tube current and the
grid drive are drastically reduced.

As an upgrade to this concept we combined both power supplies functions,
and to reduce the maximum tuning current increased the frequency of the
ac component from 60 to 180 Hz.

> **6 CONCLUSIONS**

First, the cavity and power amplifier were rigorously tested and
operated at BNL at the gap voltages exceeding the design values. The
system was designed conservatively with an eye on reliability, ease of
operation and troubleshooting in a high radiation environment. All the
components used were rated with comfortable safety margins.

**7 ACKNOWLEDGMENTS**

The authors are grateful to J.Butler and the rf technician staff for
their efforts in building the system and assistance during testing.

**8 REFERENCES**

\[1\] M.Blaskiewicz, et all, 2001 Particle Accelerator

Conference, Chicago

\[2\] F.Pederson, IEEE, TNS, Vol. NS-22, No.3, pg 1906,

(1975).

\[3\] D.Boussard, CERN 91-04 (1991)

\[4\] M.Meth, A.Zaltsman, Stability and Neutralization of

SNS RF Power Amplifier, SNS tech note #68, 1999.

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