Production and use of X-rays

A machine that wastes ninety-nine per cent of its power

• An X-ray tube run at $75\ \text{kV}$ and $30\ \text{mA}$ takes in $2250\ \text{W}$. About $99\%$ of that becomes heat in a lump of tungsten the size of a coin.
• Left alone, the target's temperature would climb at over $1000\ \text{K}$ per second and melt in a few seconds.
• That is why exposures are brief and the anode spins. The remaining one per cent is the picture.
• This lesson is how X-rays are produced, what sets their penetrating power, and how they make an image.

Production

• The four-mark answer runs in four moves, and each is a mark.
• One. Electrons are emitted from a heated filament (the cathode 阴极) by thermionic emission 热电子发射.
• Two. They are accelerated through a high p.d., tens of kV, across an evacuated tube towards a metal target 靶, the anode 阳极, usually tungsten 钨.
• Three. They decelerate rapidly when they strike the target.
• Four. The kinetic energy 动能 lost is emitted as X-ray photons 光子, this is Bremsstrahlung 轫致辐射 or braking radiation, with most of it becoming heat.

Heat one end, brake at the other

Two controls, two different jobs

• Intensity, the energy per unit area per second, is set by the number of electrons hitting the target per second, so it is controlled by the filament current. A hotter filament emits more electrons.
• Hardness 硬度, the penetrating power, is set by the photon energies, so it is controlled by the accelerating p.d. A larger p.d. gives higher-energy, shorter-wavelength, more penetrating X-rays.
• Keep them apart. A question asking how to make the beam more penetrating is not answered by turning up the current.
• A metal filter removes the softest X-rays, which would be absorbed in the patient's skin without ever reaching the detector.

The minimum wavelength

• The most energy one photon can carry is the whole kinetic energy of one electron, lost in a single event:

• This is the short-wavelength cut-off, and it depends only on the accelerating p.d., never on the target metal or the current.
• Doubling the p.d. halves the minimum wavelength.

Worked example: the cut-off at 75 kV

Reading the spectrum

• The spectrum is continuous because each electron may lose any fraction of its energy, in one deceleration or several, so photons of every energy up to the maximum appear.
• It has a sharp cut-off at $\lambda_{\text{min}}$ because no photon can carry more than one electron's energy, $eV$.
• The sharp peaks are characteristic 特征 of the target metal: an incoming electron knocks out an inner electron, an outer one falls into the vacancy, and the photon carries the difference between those two levels.
• So the curve's shape has three separate causes, and a question about it wants all three named.

A cliff, a hump, and two spikes

Sharpness and contrast are different things

• Sharpness 清晰度 is how well defined the edges are. It improves with a small source spot, a still patient, and the detector close to the patient.
• Contrast 对比度 is the difference in degree of blackening between neighbouring regions, produced by a difference in attenuation 衰减.
• The two are independent: an image can be sharp with poor contrast, or blurred with strong contrast.
• Where two soft tissues attenuate similarly, a contrast medium 造影剂 such as barium is swallowed or injected to outline one of them.

Same beam, very different shadows

Worked example: why bone shows white

The attenuation law

• Higher-energy X-rays penetrate further, meaning a smaller $\mu$; bone has a much larger $\mu$ than soft tissue.
• For a thickness, take logs: $x = \dfrac{1}{\mu}\ln\dfrac{I_0}{I}$. The half-value thickness 半值厚度 is $x_{1/2} = \ln 2/\mu$, exactly like a half-life.
• Through two layers the exponentials multiply, so add the exponents: $I = I_0 e^{-(\mu_1 x_1 + \mu_2 x_2)}$. Never add the thicknesses or the coefficients, and note the order of the layers makes no difference.
• Read the question: "what fraction is absorbed" is $1 - e^{-\mu x}$, not $e^{-\mu x}$.

Computed tomography

• A computed tomography 计算机断层扫描 (CT) scan builds a three-dimensional image, and the syllabus wants the construction described in order.
• One. Many X-ray images of the same section are taken from different angles around the patient.
• Two. A computer combines them into one two-dimensional image of that section.
• Three. The process is repeated for many sections along an axis.
• Four. The two-dimensional sections are combined into a three-dimensional image, which can be rotated or sliced on screen. The dose is far higher than a single radiograph, which is the trade-off.

Marks that slip away

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