Blum W., Riegler W., Rolandi L. Particle Detection with Drift Chambers

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320 9IonGates

9.2.2 Three Trigger Modes

The simplest case is the bipolar gating grid operated in a magnetic ﬁeld as a diode. It

does not have to be triggered, and one avoids all switching circuitry and all pick-up

problems. There is a disadvantage to this solution: although the positive ions from

the wire avalanches are not admitted back into the drift space, all the electrons from

the drift region are allowed to produce avalanches. Under conditions where chamber

ageing is a problem, one gives away a factor of the lifetime of the chamber which

depends on the background conditions of the experiment.

The tightest trigger is the one where some counters outside the drift chamber

select the wanted event and open the gate by applying a (bipolar) voltage pulse to

the grid in order to remove the closing potential(s). Depending on the time delay T

between the moment of the event and the moment the gate has been opened, one

loses a length L of sensitivity given by the electron drift velocity u:

L = T

u .

This loss can sometimes be avoided at the expense of some background – if

there is a regular time pattern when the events occur, even if they come with low

probability. The ALEPH TPC at LEP is triggered ‘open’ a few μs before every bunch

crossing of the collider. When there is no event, the gate is switched back to ‘closed’.

In this way it is ‘open’ for 6μs out of every 22μs, but it stays ‘open’ long enough to

read an event. This mode has been termed a synchronous trigger, to be contrasted

with the asynchronous trigger described in the previous paragraph. The synchronous

trigger also avoids the disturbance on the signal lines which remains large even with

a bipolar gating grid, owing to small accidental asymmetries between neighbouring

gating-grid wires.

9.3 Transparency under Various Operating Conditions

The transmission properties of a gate can be deﬁned with respect to the incoming

electrons. The electron transparency T

is the ratio between the number of electrons

traversing the grid and the number travelling towards it. In the absence of magnetic

ﬁeld, T

is given by the corresponding ratio of the numbers of ﬁeld lines. As a ﬁrst

example, we have calculated T

in Chap. 3 for the monopolar gate as a function of

the grid potential.

Similarly the ion transparency T

is the fraction of ions traversing the grid, com-

pared to all the ions travelling towards it. For the synchronous trigger mode we must

also know T

, the time-averaged ion transparency.

In this section, computed and measured transparencies are presented for the static

and for the synchronously pulsed bipolar gate, and for the bipolar gate in a magnetic

ﬁeld, operated as a diode. For the graphical representation of results and for the

comparison with measurement we use a standardized system of electrodes according

to Fig. 3.6 with wire positions as in the ALEPH TPC.

9.3 Transparency under Various Operating Conditions 321

9.3.1 Transparency of the Static Bipolar Gate

In order to describe the problem it is convenient to deﬁne two surface charge den-

sities, separating the contribution of the wires ramped at positive and negative

The (electron and ion) transparency is zero when the surface charge density of

positive charges is equal in absolute value to the surface charge density on the

high-voltage plane (or larger). The electric ﬁeld conﬁgurations for full and for zero

transparency are shown for our standard case in Fig. 9.3a,b.

To compute the potential difference

needed to close the gating grid we ﬁrst

consider the situation in which both the high-voltage plane and the zero-grid plane

are grounded. The general solution is then obtained by superimposing the solution

calculated in Sect. 3.3 when a common voltage V

is applied to the wires of the

gating grid.

Using the formalism of Sect. 3.3 it can be shown that by applying

to the

wires of the gating grid we induce a positive charge on the wires at positive potential

producing a positive surface charge density

−

. (9.7)

Fig. 9.3a,b Electric ﬁeld conﬁguration in the standard case with the bipolar gating grid. (a) gate

open, (b) gate closed

322 9IonGates

The wires at negative potential contribute to a negative surface charge density

−

= −

, (9.8)

and the total charge variation on the gating grid is 0.

This solution can be superimposed on the one calculated in Sect. 3.3.1 since it

has the same boundary conditions. The total surface charge density of the wires at

potential V

, (9.9)

where

is computed using (3.2.2).

When

/2 is positive the transparency of the gating grid is given by

T = 1 −

. (9.10)

Only half of the wires of the gating grid contribute to the positive density. This ex-

plains the factor 2 of (9.10). Formula (9.10) has been tested experimentally using

a chamber with wires arranged as shown in Fig. 3.6. We depict in Fig. 9.4a,b the

calculated and measured electron transparencies as functions of

. There is per-

fect agreement except for the large values of

where the gate was found not to

be as opaque as calculated, probably because of diffusion, which was omitted in the

calculation.

The conditions for a closed grid are

> |

| =

E , (9.11)

where E is the drift ﬁeld.

Fig. 9.4a,b Electron

transparency T (here called

)ofagatinggridwith2mm

pitch, as a function of the

voltage difference

applied to adjacent wires. The

points are measurements by

[AME 85-1]; the line is a

calculation according to

(9.10)

9.3 Transparency under Various Operating Conditions 323

When

has the limiting value for the ‘full transparency’ condition (see 3.51)

we obtain



1+ 2



. (9.12)

In the general case, using (3.53), (9.7) and (9.11) one can calculate the minimum

needed to close the grid:

> −





⎛

⎜

⎝

E −

E(z

−z

)+V

−V



−z

−



⎞

⎟

⎠

. (9.13)

Figure 9.5a-d shows how the electric ﬁeld lines are organized around the bipolar gate

as the differential voltage

is increased. We notice that for small

thegridis

partly transparent and that for larger

the ﬁeld lines from the drift region end on

the wires of the gating grid. The conﬁguration of Fig. 9.5a-db is the case where the

gate is just closed. It has ﬁeld lines from the two regions in close proximity, so that

diffusion will allow a small fraction of electrons to traverse the grid. This is not the

case in Fig. 9.5a-dc and d, where the gate is more ﬁrmly closed.

9.3.2 Average Transparency of the Regularly Pulsed Bipolar Gate

The passage of a drifting electron or ion through a gate requires some time. This time

is much longer for ions than for electrons because of their smaller drift velocity u.

Fig. 9.5a-d Electric ﬁeld

lines near the gating grid for

different values of

drift

= 110 V/cm and

= −70 V throughout. (a)

= 30 V, (b)

= 45 V,

(c)

= 100 V, (d)

= 200 V

324 9IonGates

Fig. 9.6 Regular switching of the bipolar grid at a frequency f .

T is the ‘open’ time

Since the ﬁeld region across a bipolar grid extends over some fraction of the pitch s

(see Fig. 9.5a-d) we may estimate the time to cross the gate to be roughly

= s/u , (9.14)

say between 10 and 1000μs for ions and three orders of magnitude less for electrons.

A bipolar grid can be operated at a frequency f by switching the closing voltage

during some part of every cycle so that it is ‘open’ for the remaining time

t < 1/ f ); the switching is schematized in Fig. 9.6.

t, the grid can be traversed in one cycle, and the average transparency is

T∼f

t . (9.15)

When



t, many cycles are needed to traverse the grid. The electric ﬁeld

changes many times while the ions are near the grid, and they follow a path that

alters its direction with the variation of the electric ﬁeld; see Fig. 9.7 for an illus-

tration. Each cycle, during the ‘closed’ condition, the ion makes a step towards the

gate wire at lower potential, and under favourable conditions it reaches the wire and

is absorbed.

For an accurate computation of the transparency we would have to follow the

relevant ﬁeld lines at every step. But we are satisﬁed with an order-of-magnitude

Fig. 9.7 Sketch of the ion

path near the gating grid

pulsed at some frequency

9.3 Transparency under Various Operating Conditions 325

calculation, which will exhibit the main variables and their inﬂuence on the average

ion transparency.

We call the effective depth of the grid S – it will be some fraction of the pitch

s – and we assume that the drift ﬁeld E

acts all the time whereas the transverse

ﬁeld E

between the wires of the gating grid acts only during the time the gate is

closed.

Assuming that an ion needs n cycles for the traversal of the grid,

n =

, (9.16)

it is absorbed if

< n



−



. (9.17)

Here v

and v

are the two components of the drift velocity and x

is the initial

transverse distance of the ion from the closest gating wire at lower potential (see

Fig. 9.7).

The transparency is zero if

s <



−



, (9.18)

where s is the pitch of the gating grid.

We can calculate the transparency in the general case assuming that the ions are

uniformly distributed along x when they reach the region of the gating grid. Using

(9.16) and (9.17) we obtain

T = 1 −

(1− f

t) . (9.19)

Since the drift velocity of the ions is proportional to the electric ﬁeld, the ratio

between its components can be replaced by the ratio between the components of

the electric ﬁeld. The z component of the electric ﬁeld is the drift ﬁeld E

and the

x component can be approximated by 2

/s. We obtain for the time-averaged ion

transparency

T = 1 −

(1− f

t) . (9.20)

Equation (9.20) shows that within the limits of our very coarse approximations, the

average transparency is a linear function of

and the frequency f.Thisisalso

borne out by experiment: in Figs. 9.8 and 9.9 we see the result of measurements

[AME 85-2] made with a gating grid operating under conditions similar to those of

the ALEPH TPC. Formula (9.20) describes both curves quite well with values of

S/s between 0.4 and 0.5.

326 9IonGates

Fig. 9.8 Average

transparency T for ions

through a bipolar grid with a

pitch 2 mm, which was pulsed

at 100 kHz with an ‘open’

time of 6μs, and a ‘closed’

time of 4μs, as a function of

the voltage difference

applied to adjacent wires. The

points are measured by

[AME 85-2]; the straight line

was drawn to connect the

points

9.3.3 Transparency of the Static Bipolar Gate in a Transverse

Magnetic Field

A magnetic ﬁeld along the main drift direction z changes the path of the electrons

according to the parameter

ωτ

; see (2.6). The components u

of the drift velocity

perpendicular to the magnetic ﬁeld and perpendicular to the grid wires is reduced

by the factor 1 +

, whereas the drift velocity u

in the main direction stays the

same:

= μE

(9.21)

Fig. 9.9 Average

transparency T for ions

through a bipolar grid (pitch

2 mm), which was pulsed

with

= ±45 V for a

constant ‘open’ time of 6μs,

as a function of the frequency.

The points are measured by

[AME 85-2]; the straight line

was drawn to connect the

points

9.3 Transparency under Various Operating Conditions 327

Here

is the electron mobility. We see that there is a strong inﬂuence of the mag-

netic ﬁeld on the operation of the bipolar gate – it is closed at much higher values

, since the relevant drift-velocity component u

, which moves the electrons

towards the wires of the grid, is reduced.

We can construct the drift trajectories when we know the behaviour of

ωτ

with

the electric ﬁeld strength E. This could be calculated according to the principles

discussed in Sect. 2.2.3. But for our example we simply use

ωτ

= 6(T

−1

)B for E < 100V/cm ,

ωτ

= 6(T

−1

)B100(V/cm)/E for E > 100V/cm .

Figure 9.10a-d shows the electron drift lines in the x–z plane for a number of

conditions. The electron transparency is computed counting the fraction of drift ve-

locity lines that cross the grid. Comparing Figs. 9.10a-da and b, one observes that

the magnetic ﬁeld of 1.5 T changed the transparency from zero to about 80%.

Figure 9.11 displays the measured electron transparency of a gating grid with a

pitch of 2 mm in a drift ﬁeld of 100 V/cm for different values of the magnetic ﬁeld

[AME 85-1]. One observes that the closing voltage goes up roughly linearly with

the magnetic ﬁeld.

Displacement of the Electrons along the Wire Direction. The electrons cross the

gating grid in the presence of a component (x) of the electric ﬁeld perpendicular

to the magnetic ﬁeld. Owing to the E ×B term of the drift-velocity equation (2.6)

Fig. 9.10a-d Electron

trajectories approaching the

grid from the drift region.

E = 110 V/cm. (a)

= 45 V, B = 0, (b)

= 45 V, B = 1.5T,(c)

= 70 V, B = 1.5T,(d)

= 200 V, B = 1.5T

328 9IonGates

Fig. 9.11 Electron

transparency vs.

(here

called

V) for various

magnetic ﬁelds, as measured

by [AME 85-1]. The lines are

drawn to guide the eye. The

two squares show the result of

calculations according to

Sect. 9.3.3

they are also displaced along the direction (y) parallel to the wires of the grid. The

component of the drift velocity along the wire direction is

ωτ

This effect is similar to the displacement of the electrons along the sense-

wire direction when they approach the sense wire from the zero-grid region (see

Sect. 7.3.1).

Figure 9.5a-db shows the electric ﬁeld lines in the region of the gating grid when

the grid is closed for the ions (but not for the electrons if a strong magnetic ﬁeld is

present). The electric ﬁeld is roughly constant between two sides of the grid, and its

x component changes sign on the two sides of the same wire. All the electrons that

cross the grid on the same side of a given wire are displaced along y in the same

direction and roughly by the same amount; all the others that pass on the other side

are displaced by the same amount but in the opposite direction. This displacement

can be of the order of fractions of a millimetre and depends on

, on the magnetic

ﬁeld and on the gas mixture.

The distribution of the arrival point of the electrons on the sense wire is modiﬁed.

This effect inﬂuences the spatial resolution in a similar way as the E ×B effect at

the sense wire.

If the pitch of the gating grid and the sense-ﬁeld grid are the same, it is pos-

sible to choose the sign of

in such a way that the y displacement at the

gating grid has sign opposite to the y displacement at the sense wire [AME 86].

In this case there is a compensation of the overall E × B effect with a pos-

sible beneﬁt to the spatial resolution; nothing quantitative has appeared in the

literature.

References 329

References

[AME 85-1] S.R. Amendolia et al., Inﬂuence of the magnetic ﬁeld on the gating of a time

projection chamber, Nucl. Instrum. Methods Phys. Res. A 234, 47 (1985)

[AME 85-2] S.R. Amendolia et al., Ion trapping properties of a synchronously gated time pro-

jection chamber, Nucl. Instrum. Methods Phys. Res. A 239, 192 (1985)

[AME 86] S.R. Amendolia et al., Gating in the ALEPH time projection chamber, Nucl. In-

strum. Methods Phys. Res. A 252, 403 (1986) and CERN-EF preprint 84–11 (1984)

(unpublished)

[BEI 88] S.P. Beingessner, T.C. Meyer, M. Yvert, Inﬂuence of chemical trace additives on

the future ageing of the UA1 Central detector. Nucl. Instrum. Methods Phys. Res.

A 272, 669 (1988)

[BRE 80] A. Breskin, G. Charpak, S. Majewski, G. Melchart, A. Peisert, F. Sauli, F. Mathy,

G. Petersen, High ﬂux operation of the gated multistep avalanche chamber, Nucl.

Instrum. Methods 178, 11 (1980)

[BRY 85] D.A. Bryman et al., Gated grid system used with a time projection chamber, Nucl.

Instrum. Methods Phys. Res. A 234, 42 (1985)

[KEN 84] Joel Kent, Positive ion suppression with untriggered TPC; College de France

Preprint 84–17 (1984) (unpublished)

[NEM 83] P. Nemethy, P.J. Oddone, N. Toge, A. Ishibashi, Gated time projection chamber,

Nucl. Instrum. Methods Phys. Res. 212, 273 (1983)