A Very Low Temperature Vibration Isolation System - CiteSeerX

A Very Low Temperature Vibration Isolation System* E.W. Hudson, R.W. Simmonds, C.A. Yi Leon, S.H. Pan, and J.C. Davis Department of Physics, University of California at Berkeley Berkeley, CA 94720, USA Very low temperature refrigerators are a significant source of low frequency vibrational and acoustic noise, which is a serious challenge to research using high sensitivity mechanical oscillators, or to high resolution scanning tunneling microscopes. We describe the design and operation of a vibration isolation system which is used at very low temperatures. The system consists of four masses suspended one below the other from the base of the refrigerator, on a series of springs. Eddy current dissipation is used to damp the motion, and thermal contact is made through an annealed copper ribbon. The plate which holds the experimental apparatus can be held rigidly in position, or released, by use of clamps actuated with superfluid 4He.

1. INTRODUCTION Vibration isolation is commonly used to isolate an experiment from the lab’s noisy environment. Unfortunately, for low temperature experiments, it is often the cryogenic process itself (boiling nitrogen and helium and the pings of contracting materials), which produces troublesome vibrations. In such cases, isolation from the noisy environment, namely the refrigerator, is often difficult and at odds with the strong contact required for thermal reasons. We have designed and constructed an isolation system which is mounted below the final stage of a 3He sorption refrigerator. Since the system is used to isolate a very low temperature scanning tunneling microscope, we are mostly concerned with eliminating high frequency modes which might excite the rather stiff scanner. a Springs b Masses c He actuated bellows d Support (T=0.24K)

2. DESIGN The isolation system consists Figure 1: A four stage of three main parts: a collection system for vibration of springs, masses and dampers, isolation with 4He a clamp which can turn off and

on the isolation by firmly holding or gently releasing the final isolation stage, and an annealed copper ribbon which gently loops from stage to stage. Figure 1 is a simple schematic of the system. Aside from the minimal thermal contact through the springs, all heat is removed from the final plate through a highly annealed piece of OFHC ribbon, 0.010” thick and 1/2” wide, which is bolted both to the 3He pot and to each of the stages of the vibration isolation system. Annealing the ribbon serves two purposes -- it both softens it, thus reducing its effect on the isolation, and it increases its thermal conductivity by several orders of magnitude, allowing the ribbon to deal with all heat generated on these stages. With the isolation activated, the final stage was cooled to 0.24 K. The clamps are operated with hydraulically actuated bellows, pressurized with superfluid 4He. Although 4He provides some additional heat load to the 3He fridge, its low heat capacity at these temperatures makes it a better choice than 3He. 3. VIBRATION ISOLATION MODEL We modeled the response of the vibration isolation system by treating it as a four stage, one dimensional harmonic oscillator with damping [1]. For such a model, frequency response may be determined by r r inverting the matrix equation Ax = c1 X .

activated clamps. *

Supported by the National Science Foundation and the Packard Foundation

Here, A is given by: − m1 w 2 + (c1 + c2 )  A=     

− c2 0 − m2 w 2 + (c2 + c3 ) − c3 − c3 − m3 w 2 + (c3 + c4 )

− c2 0 0

− c4

0

     − m4 w 2 + c4   0 0 − c4

cn = k n + iω bn contains information about both the spring constant (kn) between stages (n-1) and n (with mass mn) as well as the damping constant between those stages (bn). r x is a vector containing the resultant amplitude of motion of each stage at a gen frequency ω and v X = ( X 0 0 0 0 ) is a vector indicating that all

4

10

Damped Vib.Iso.

RMS Motion (Angstroms)

3

motions are driven from the initial stage with magnitude X0. Thus, the transfer function for the isolation is given x −1 . by: Z = 20 log10 4 = 20 log10 A 41 X0

Undamped Vib.Iso.

10

No Vib.Iso.

2

10

1

10

0

10

-1

10

-2

10

-3

Noise Floor of Preamplifier

10

40 Transfer Function (dB)

The signal is amplified by a home built preamplifier with a gain of 104 and a noise floor of 3 nv / Hz above 25 Hz and measured on a HP 35670A dynamic signal analyzer. Voltages were converted to rms displacements using the known response function of the accelerometers. Typical motion of the final stage is plotted in figure 3.

0

10

0

1

10 Frequency (Hz)

2

10

Figure 3: Experimental motion of final plate in vibration isolation system, with and without damping, compared to motion with the plate clamped to the fridge.

-40 -80 Heavily Damped System

-120

Undamped System

-160 -200 -1 10

10

0

1

2

10 10 Frequency (Hz) Figure 2: Theoretical transfer function for a four stage vibration isolation system.

Two important facts about such a response should be noted. First of all, there are 4 resonance peaks (one for each stage), with the lowest somewhere above f low =

1 2π

g l

, where g is the acceleration due to

gravity, and l is the maximum extension length of the spring system. In order to keep all resonances as low as possible, one needs to cascade values for kn, as the springs support less and less weight as n increases. Secondly, above the 4th (final) resonance, response falls off at between 20 and 40 dB per decade of frequency per stage, depending on the strength of damping. 3. RESULTS Experimental vibration levels were measured with accelerometers from Oyo Geospace [2]. These sensors have been used reliably at temperatures as low as 5 mK in our labs.

4. DISCUSSION The response of our system is much more complicated in practice than in theory, due to horizontal modes and triangular symmetry. However, our approximations provided us with a fairly accurate picture of the strongest resonances of the system, and allowed us to estimate the amount of damping required. As can be seen in figure 3, damping is crucial in bringing down low frequency resonance amplification. Between 0.5 Hz and 20 Hz, the integrated rms motion of the damped system is 6 µm rms, compared to 12 µm rms for the undamped system, and 0.7 µm rms without isolation. Above 20 Hz, our measurements with isolation are limited by the noise floor of the amplifier. Between 20 and 100 Hz, integrated rms motion is less than 1.5 A& for both systems with isolation, compared to 0.6 µm rms without isolation. And above 100 Hz, rms motion for the systems with isolation is below 10-3 A& . REFERENCES [1] C. Julian Chen: Introduction to Scanning Tunneling Microscopy (New York: Oxford University Press, 1993). [2] HS-J 7.5 Hz, 300 Ohm Geophone, Oyo Geospace, Houston, TX, USA.