NPA/Int. 66-24 * Meyrin, December 1966.

DETECTION OF MICROPARTICLES USING A LASER BEAM

I.

INTRODUCTION

The object of an investigation currently in progress in the N. P.A. Division is the detection of microparticles of matter which, it is sometimes considered, contribute to vacuum breakdown.

In traversing a laser beam such particles

will scatter the laser light and the scattered radiation can be detected using a photomultiplier or photodetector,

The signal produced by the photomultiplier

would indicate the presence of and disclose the velocity of a microparticle, from which it should be possible to deduce its charge to mass ratio. The following discussion attempts to examine on a quantitative basis the most significant parameters which determine whether a microparticle of given size can be detected with a given laser and photomultiplier system.

II.

MICROPARTICLE VELOCITY AND BEAM TRANSIT TIME

For simplicity we suppose that the microparticles are spherical in shape and that they acquire the same surface charge density as the electrode on which they initially rest.

If the electric field intensity is E, the surface density of

charge o on the particle is given by E = 4·,; J microparticle is 4

n/

•

where r is its radius.

The surface area of the If the microparticle is

uniformly charged the total charge Q on it is o 4 n r 3 h 4 , ·1 , by m = p 3 t h e m1cropart1c e ,is given nr w ere p material of the microparticle.

Q m

2

=

2

Er .

The mass of

is the density of the

The charge to mass ratio Q/m is thus given by 3E =

4n rp

------ (1)

On the electrode surface the microparticle experiences the electrostatic force

*

This is a revised version of a report written in September 1966.

- 2 -

due to the applied field and when it moves its equation of motion will be m dv dt

QE

so that the microparticle velocity rest at t = 0,

v = Q

Et

m

assuming that it starts from

The distance S travelled, measured from the electrode, in a

time t is

s

t

=

2

----- (2)

2

m

The laser beam can (but need not necessarily) be aligned along the central section of the vacuum gap,

Le. S = d/2 in a gap of width d,

In this case the

time ti taken for the particle to get to this central position is given by setting 2

S = d/2 in the above equation,

i.e. 1

(~

m ) 2

-- -- ( 3)

Q

E

and the velocity v 1 of the microparticle at the centre of the gap is given by 2 =

g

=

m

----- (4)

=

where V = Ed is the voltage applied to the gap, If the laser beam width is W the particle transit time (neglecting its acceleration during the time

T

b

"' W/

1

=

W

2

A typical value of

T

1[34 EV J

2

6

=

b through it

b) will be roughly W /V!

1

rrrp

b is 5 x 10 -

T

T

W

l3l4

E2 d] rr r p

!

,

i, e,

----- (5)

second for a particle of radius 10

-5

cm

traversing a laser beam 0, 1 cm wide in a vacuum gap of 1 cm in which the electric field is 10 5 v cm -l,

- 3 -

IIL ENERGY SCATTERED BY SPHERICAL MICROPARTICLE

As the microparticle traverses the laser beam on an assumed orthogonal path it scatters the laser light during the time Tb.

This is equivalent to

flash illumination of the microparticle by the laser beam for a time T b

0

Suppose that the beam power is P and let area of cross-section of the beam be A.

We will assume that the power density

cross section of the microparticle is beam for the time

I

i

is uniform.

If the optical

it will intercept a fraction

I /A of the

1b and the energy scattered by the microparticle in

traversing the beam is given approximately by

When the photon detector is placed at a distance L from the point of scattering, and, if isotropic scattering occurs, the energy received per square centimeter at the detector will be approximately p I 'b

If the effective aperture of the

0

A 4 rrL2

detector is

a,

(Le if it has a sensitive area 0

a

),

~

the energy

received by

the detector will be

=

------ (7)

IVo PHOTON FLUX AT DETECTOR We can now estimate, for a laser of given beam power density P/A and radiation of wavelength during the time 'b

0

>c ,

the number N of photons received by the detector

We note that the energy received,

~

=

where v

is the radiation frequency,

of lighto

Thus the number of photons received during the time

N

=

NhV

=

Nh c/A

h is Planck's constant and c is the velocity

p I Tb

A

4rrL2

1

b

is

a;\

he-

- - - - -- (8)

- 4 -

It may be computationally more convenient to express equation (8) in terms

of W, the laser beam width, using A=

2 'TTW /4, giving T

N

=

b

,\

photons.

-- --- - (9)

he

If the detector used is a photomultiplier its sensitivity is usually quoted as S( ,\) or as Nkr in milliamperes/watt or as photoelectrons emitted per photon

arriving at its cathode . Now, using equation (7), the power arriving at the photomultiplier is watts ,

------ (10)

and this would give rise to a cathode emitted current of

=

=

Nkr Pfo

x

10 - 3 ------ (11)

A 4'TTL 2 and the photomultiplier anode sign2J current would be =

GI

k

=

GN kr

p Ea

x

amperes,

------ (12)

A'TT 4 L

where G is the photomultiplier gain for the given value of its anode pote.q.tial.

V.

PARAMETERS GOVERNING THE MINIMUM DETECTABLE MICROPARTICLE SI/E A photomultiplier is a power sensitive device and equation ( 10) gives the power

received by the photomultiplier as

(

independent of the particle transit time

~

p Ea. I , b) = A 4 'TT L 2

watts.

This is

0

If the spectral sensitivity of the photomultiplier at the laser wavelength A S( ,\) mA/'Natt and the gain is G then the anode signal will be

X 4!aL 2

is

S (A ) G ·

- 5 -

Clearly this must exceed the noise generated in the detector, detection of a particle of optical cross section I p

Ia

A 4rrL2 ID is the anode dark current,

The criterion for

is thus

S( 1' ) G

S

- -- - - - ( 13)

is the signal to noise ratio.

It follows from equation (13) that the minimum detectable optical scattering

cross-section is I

given by the relation >

I S A D

------ (14)

P aS(J

------ (15)

Clearly (P /A) the laser beam power density and a the photomultiplier sensitive area must be made as large as possible.

The photomultiplier should be

chosen to have a large value of spectral sensitivity S( >--

>--

)

for the laser wavelength

The quantities G, S (A. ) and a are, of course, fixed once the photo-

multiplier is selected.

The distance L must obviously be made as small as is

conveniently possible . Provided the wavelength radius r the value of

I

>--

is of the same order or less than the micro-particle

will be given by

I

2

= rr r , but for values of

(r/>--) ::; 0 .5 diffraction effects and Raleigh scattering, with I proportional to ··4 >-, make I become vanishingly small. (See "Propagation of Short Radio Waves" in Vol.13 M .I. T. Radiation Laboratory Series, McGraw Hill, 1951). The remaining parameter of importance is ID, the anode dark current.

This

is governed by the temperature of the photomultiplier and a considerable gain in

- 6-

sensitivity can be obtained - perhaps by a factor of about a hundred-fold, by cooling with Dry- Ice,

VI. SENSITIVITY OF THE EXISTING SPECTRA PHYSICS LASER AND PHILIPS PHOTOMULTIPLIER

The present available continuous wave laser in N. P.A. Division is a Spectra Physics He-Ne laser with a power output P " 0, 3 x 10 - 3 watt and a beam width of

"0 .2 cm.

The photomultiplier used is a Philips 56 AVP which has a sensitive

cJameterof 4.2cm,

i.e.

o:

2

"14cm.

In W.F.Gunn'sapparatusthephoto-

multiplier is located about 5 cm from the point where the iron filings of radius r -3 2 enter the laser beam, i.e. L = 5 cm, Thus ( ~ /Tb) "' 1. 33 x 10 r watts. The spectral sensitivity of the 56 AVP at the He-Ne laser radiation wavelength 0

is only about 3% of its maximum sensitivity which occurs at 4, 400 A. -3 0 S( A ) 55 x 10 A/watt at 4, 400 A. Thus the "effective power" -5 2 " 4 x 10 r watts, and the photomultiplier cathode current produced will be -6 2 A if the photoabout 2.2 x 10 r A and the anode current will be about 220

r2

multiplier gain is 10 8 The maximum quoted anode dark current for the uncooled photomultiplier is

5 x 10

-6

A and the anode current must exceed this, i . e. r

>

1 . 5 x 10

-4

cm.

Consequently, the minimum detectable iron filing in W .F. Gunn's apparatus will be one having a radius which just exceeds 1. 5 x 10 - 4 cm if we assume a signal to noise ratio

S of unity.

This value of S is unreasonably small and

S

2 or

perhaps even 10 will be necessary, in which case the radius of the smallest detectable particle increases by about 1 . 4 or by about 3. 2 .

- 7 -

VII.

APPLICATION TO MODEL CHAMPAGNE

Using known characteristics of photomultipliers and the known dimensions of Champagne we can estimate the minimum laser beam power density needed to -4 -4 detect a particle having a radius of 10 cm, i.e. r = 10 cm and -8 2 L: = TI 10 cm . An estimate of the minimum value of L is about 30 cm.

The reflected

power is thus, using equation (10), TI

p

A

10

-10

watts.

if we use the largest available RCA photomultiplier which has a spectral sensitivity of 30 mA/watt, a gain of 1. 5 x 10 5 and a sensitive area of about 120 cm 2 . In this case the photomultiplier anode current is about

-6

1. 5 P 10 A. A This signal should be at least twice or three times the dark current at the anode.

RCA do not provide a figure for this but we will assume that it is about 10

i.e.

p A

-6 A

2

2 watts/cm .

The existing He-Ne laser in CERN has a power density of only about 5 x 10 - 3 watts/ cm 2 and even with cathode r ooling of the photomul ti plier it is clearly insufficiently powerful to detect a micron sized particle. Continuous wave 40 watt/cm 2 GJ 2 lasers are commercially available and could be used for the detection of micron sized particles thus avoiding the :::ynchronisation difficulties which would arise in attempting to use c: 71Jsed ruby laser. The un-Q-switched Bradley ruby laser could also be used since it has a power density PIA of about 10 5 watts/cm 2 but again synchronisation of laser action with particle transit will be difficulL

However, if the microparticles are always

- 8-

present - moving to and fro between the electrodes, they should be easily detectable with the ruby laser without any synchronisation being necessary. Using equation (15) and the known characteristics of the largest available RCA photomultiplier (5" diameter) S( >. ) = 30 mA/watt, G = 1.5 x 10 5 and of the Philips 56 TVP photomultiplier the minimum values of continuous wave laser beam power density have been estimated for various values 1 ~ (3 ~ 10 of the signal to noise ratio

13

assuming an anode dark current of 1

results are given in the table,

µ

A.

The

This indicates that for our purposes the Philips

56 TVP tube is easily the best and could, with a 10 watt

co 2 laser,

detect

particles as small as 10 - 5 cm radius.

I

R .C .A. Photomultiplier

Philips 56 TVP

-

II

-----

-2 PIA watts cm

r=lO

(3

-5

cm

-2 66w.cm

1

r==1·o-4 cm

r=lO

-3

0.66

6 .6xl0

cm -3 -2

2

132

l. 32

L32xl0

3

200

2

2 x 10- 2

10

660

6.6

6 .6xl0

-2

r=lO

-5

cm

r=lO

-4

cm

r=lO

-3

cm

2

2 x 10- 2

2 x 10- 4

4

4 x 10- 2

4 x 10- 4

6

6 x 10- 2

6 x 10- 4

20

0.2

2 x 10- 3

I C. GJr..ey :.foJr..gan